+
    ‰°³já>  ã                   ó  € ^RI HtHt R t]R 4       t]R 4       t]R 4       t]R 4       t]R 4       t ]R 4       t	]R	 4       t
]R
 4       t]R 4       t]RR l4       t]RR l4       t]R 4       t]R 4       t]R 4       tR# )é   )ÚdefunÚdefun_wrappedc                óÂ  € V P                  V4      w  rV P                  V4      pV P                  ) pV'       gS   ^V P                  .VR.. WQ^,
          ,          .. . ^ 3pV'       d#   V^,          ^ ;;,          WQ,          ,          uu&   V3# V P	                  V) 4      ;'       gM    V P                  V4      ^ 8„  ;'       g1    V P                  V4      ^ 8H  ;'       d    V P                  V4      ^ 8„  pV P                  ^,          ^,           pV'       dK   V P                  V P                  W"VR7      RRR7      p	V P                  W P                  RVR7      VR7      p
MTp
V P                  WªVR7      pV P                  ^W¸R7      pV P                  VRR7      pV P                  V
RR7      pV'       d&   ^V
.W.. . WQ,          WQ^,
          ,          .. V3pV.pMb^V.W.. . WQ,          WQ^,
          ,          .. V3p^V P                  V.V^,           R^.. WQ,          .WQ^,
          ,          .^V,
          .V3pVV.pV'       d”   V P                  X	4      p\        \        V4      4       Fj  pVV,          ^,          ^ ;;,          WQ,          ,          uu&   VV,          ^ ,          P                  V4       VV,          ^,          P                  ^4       Kl  	  \!        V4      # )z„
Combined calculation of the Hermite polynomial H_n(z) (and its
generalization to complex n) and the parabolic cylinder
function D.
ç      à?)ÚprecT©Úexactç      Ð¿)Ú_convert_paramÚconvertÚmpq_1_2ÚpiÚisnpintÚreÚimr   ÚfmulÚsqrtÚfdivÚfnegÚexpÚrangeÚlenÚappendÚtuple)ÚctxÚnÚzÚparabolic_cylinderÚntypÚqÚT1Úcan_use_2f0ÚexpprecÚuÚwÚw2Úrw2Únrw2ÚnwÚtermsÚT2ÚexpuÚis   &&&&               Ú\/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/functions/orthogonal.pyÚ_hermite_paramr/      s|  € ð × Ñ  Ó#�G€AØ�‰�A‹€AØ	�‰ˆ€A÷  Ø�—‘ˆ[˜1˜c˜( B¨¨a­C­¨	°2°r¸1Ð<ˆßØˆq�E�!�H˜��O‹HØˆsˆ
Ø—+‘+˜q˜b“/÷ +ð + S§V¡V¨A£Y°¡]÷ +ð +Ø	�‰�‹�a‰×	)Ð	)˜CŸF™F 1›I¨™Mð à�h‰h�q�j˜2�o€GßØ�H‰H�S—X‘X˜a w�XÓ/°¸dˆHÓCˆØ�H‰H�QŸ™ ¨'˜Ó2¸ˆHÓA‰àˆØ	�‰�!˜WˆÓ	%€BØ
�(‰(�1�bˆ(Ó
'€CØ�8‰8�C˜tˆ8Ó$€DØ	�‰�!˜4ˆÓ	 €BßØ�ˆV�a�V˜R  a¥c¨1°­c­7 ^°R¸Ð=ˆØ�‰à�ˆW�q�f˜b " q¥s¨A°­s­G n°b¸$Ð>ˆØ�—‘˜ˆ_˜q �s C¨˜m¨R°!µ#°¸¸a½C½¸	ÀAÀaÅCÀ5È"ÐLˆØ�B�ˆçØ�w‰w�q‹zˆÜ”s˜5“zÖ"ˆAØ�!�H�Q�K˜�N˜a�cÕ!‹NØ�!�H�Q�K×Ñ˜tÔ$Ø�!�H�Q�K×Ñ˜qÖ!ñ #ô �‹<Ðó    c                 ó<   a aa€ S P                   ! V VV3R  l. 3/ VB # )c                  ó    <€ \        S SS^ 4      # )é    ©r/   ©r   r   r   s   €€€r.   Ú<lambda>Úhermite.<locals>.<lambda>>   ó   ø€ ¤°°Q¸¸1Ô!=r0   ©Ú	hypercomb©r   r   r   Úkwargss   fff,r.   Úhermiter=   <   s   ú€ à�=Š=Ö=¸rÑLÀVÑLÐLr0   c                ó<   a aa€ S P                   ! V VV3R l. 3/ VB # )a¤  
Gives the parabolic cylinder function in Whittaker's notation
`D_n(z) = U(-n-1/2, z)` (see :func:`~mpmath.pcfu`).
It solves the differential equation

.. math ::

    y'' + \left(n + \frac{1}{2} - \frac{1}{4} z^2\right) y = 0.

and can be represented in terms of Hermite polynomials
(see :func:`~mpmath.hermite`) as

.. math ::

    D_n(z) = 2^{-n/2} e^{-z^2/4} H_n\left(\frac{z}{\sqrt{2}}\right).

**Plots**

.. literalinclude :: /plots/pcfd.py
.. image :: /plots/pcfd.png

**Examples**

    >>> from mpmath import *
    >>> mp.dps = 25; mp.pretty = True
    >>> pcfd(0,0); pcfd(1,0); pcfd(2,0); pcfd(3,0)
    1.0
    0.0
    -1.0
    0.0
    >>> pcfd(4,0); pcfd(-3,0)
    3.0
    0.6266570686577501256039413
    >>> pcfd('1/2', 2+3j)
    (-5.363331161232920734849056 - 3.858877821790010714163487j)
    >>> pcfd(2, -10)
    1.374906442631438038871515e-9

Verifying the differential equation::

    >>> n = mpf(2.5)
    >>> y = lambda z: pcfd(n,z)
    >>> z = 1.75
    >>> chop(diff(y,z,2) + (n+0.5-0.25*z**2)*y(z))
    0.0

Rational Taylor series expansion when `n` is an integer::

    >>> taylor(lambda z: pcfd(5,z), 0, 7)
    [0.0, 15.0, 0.0, -13.75, 0.0, 3.96875, 0.0, -0.6015625]

c                  ó    <€ \        S SS^4      # ©r   r4   r5   s   €€€r.   r6   Úpcfd.<locals>.<lambda>v   r8   r0   r9   r;   s   fff,r.   ÚpcfdrB   @   s   ú€ ðl �=Š=Ö=¸rÑLÀVÑLÐLr0   c                óp   € V P                  V4      w  rEV P                  V) V P                  ,
          V4      # )ae  
Gives the parabolic cylinder function `U(a,z)`, which may be
defined for `\Re(z) > 0` in terms of the confluent
U-function (see :func:`~mpmath.hyperu`) by

.. math ::

    U(a,z) = 2^{-\frac{1}{4}-\frac{a}{2}} e^{-\frac{1}{4} z^2}
        U\left(\frac{a}{2}+\frac{1}{4},
        \frac{1}{2}, \frac{1}{2}z^2\right)

or, for arbitrary `z`,

.. math ::

    e^{-\frac{1}{4}z^2} U(a,z) =
        U(a,0) \,_1F_1\left(-\tfrac{a}{2}+\tfrac{1}{4};
        \tfrac{1}{2}; -\tfrac{1}{2}z^2\right) +
        U'(a,0) z \,_1F_1\left(-\tfrac{a}{2}+\tfrac{3}{4};
        \tfrac{3}{2}; -\tfrac{1}{2}z^2\right).

**Examples**

Connection to other functions::

    >>> from mpmath import *
    >>> mp.dps = 25; mp.pretty = True
    >>> z = mpf(3)
    >>> pcfu(0.5,z)
    0.03210358129311151450551963
    >>> sqrt(pi/2)*exp(z**2/4)*erfc(z/sqrt(2))
    0.03210358129311151450551963
    >>> pcfu(0.5,-z)
    23.75012332835297233711255
    >>> sqrt(pi/2)*exp(z**2/4)*erfc(-z/sqrt(2))
    23.75012332835297233711255
    >>> pcfu(0.5,-z)
    23.75012332835297233711255
    >>> sqrt(pi/2)*exp(z**2/4)*erfc(-z/sqrt(2))
    23.75012332835297233711255

)r   rB   r   )r   Úar   r<   r   Ú_s   &&&,  r.   ÚpcfurF   x   s2   € ðX ×Ñ˜aÓ �D€AØ�8‰8�Q�B�s—{‘{•N AÓ&Ð&r0   c                óÊ  a aaaa	€ S P                  V4      w  opS P                  S4      oS P                  oS P                  o	VR8X  d~   S P	                  S^,          4      '       d`   V VVV	V3R lpS P
                  ! V. 3/ VB pS P                  S4      '       d)   S P                  S4      '       d   S P                  V4      pV# V VV	V3R lpS P
                  ! VS.3/ VB # )a‚  
Gives the parabolic cylinder function `V(a,z)`, which can be
represented in terms of :func:`~mpmath.pcfu` as

.. math ::

    V(a,z) = \frac{\Gamma(a+\tfrac{1}{2}) (U(a,-z)-\sin(\pi a) U(a,z)}{\pi}.

**Examples**

Wronskian relation between `U` and `V`::

    >>> from mpmath import *
    >>> mp.dps = 25; mp.pretty = True
    >>> a, z = 2, 3
    >>> pcfu(a,z)*diff(pcfv,(a,z),(0,1))-diff(pcfu,(a,z),(0,1))*pcfv(a,z)
    0.7978845608028653558798921
    >>> sqrt(2/pi)
    0.7978845608028653558798921
    >>> a, z = 2.5, 3
    >>> pcfu(a,z)*diff(pcfv,(a,z),(0,1))-diff(pcfu,(a,z),(0,1))*pcfv(a,z)
    0.7978845608028653558798921
    >>> a, z = 0.25, -1
    >>> pcfu(a,z)*diff(pcfv,(a,z),(0,1))-diff(pcfu,(a,z),(0,1))*pcfv(a,z)
    0.7978845608028653558798921
    >>> a, z = 2+1j, 2+3j
    >>> chop(pcfu(a,z)*diff(pcfv,(a,z),(0,1))-diff(pcfu,(a,z),(0,1))*pcfv(a,z))
    0.7978845608028653558798921

ÚQc                  ó@  <€ SP                  S	RRR7      p \        SS) S,
          S	^4      p\        SSS,
          V ^4      pV FR  pV^ ,          P                  R 4       V^,          P                  ^4       V^,          P                  SS,
          4       KT  	  SP                  SS,          S,
          4      SP	                  ^SP
                  ,          4      ,          pV F3  pV^ ,          P                  V4       V^,          P                  ^4       K5  	  W,           # )ù              ð?Tr   y       €      ð¿)r   r/   r   Úexpjpir   r   )
ÚjzÚT1termsÚT2termsÚTr$   r   r   r    Úrr   s
        €€€€€r.   ÚhÚpcfv.<locals>.hÍ   sÞ   ø€ Ø—‘˜!˜S¨�Ó-ˆBÜ$ S¨1¨"¨Q­$°°1Ó5ˆGÜ$ S¨!¨A­#¨r°1Ó5ˆGÛ�Ø�!•—‘˜B”Ø�!•—‘˜A”Ø�!•—‘˜A˜a�CÖ ñ ð —
‘
˜A˜a�C �EÓ# c§h¡h¨q°·±­xÓ&8Õ8ˆAÛ�Ø�!•—‘˜A”Ø�!•—‘˜A–ñ ð Õ$Ð$r0   c                 óø  <€ S
P                  SR4      pS
P                  SR4      pS
P                  V4      pS
P                  SS
P                  V4      .pVS) V S,          S,           ^.SSV ,          ,
          .. SV ,          S,           .S.V3pVS.,           S) V S,          S,
          ^^.^S,
          SV ,          ,
          .. SV ,          ^,           S,
          .^S,           .V3pS
P                  SSV ,          ,           4      w  rxV^ ,          P	                  V4       V^ ,          P	                  V4       WV3 F:  p	V	^,          P	                  ^4       V	^,          P	                  SV ,
          4       K<  	  WV3# )ç      Ð?r   r
   )Úsquare_exp_argr   r   Úcospi_sinpir   )r   r%   r$   ÚeÚlÚY1ÚY2ÚcÚsÚYr   r    rP   r   s   &         €€€€r.   rQ   rR   ß   sC  ø€ Ø×"Ñ" 1 eÓ,ˆAØ×"Ñ" 1 cÓ*ˆAØ—‘˜“
ˆAØ—‘˜˜CŸG™G A›JÐ'ˆAØ�a�R˜˜1�˜Q� �N Q q¨¥s¥U G¨R°!°Aµ#°aµ%°¸1¸#¸qÐ@ˆBØ�a�S•˜A˜2˜q �s 1�u a¨Ð+¨a°­c°!°Aµ#­g¨Y¸¸Q¸q½SÀ½UÀ1½W¸IÈÈ!ÍÀuÈaÐOˆBØ—?‘? 1 Q q¥S¥5Ó)‰DˆAØˆq�E�L‰L˜ŒOØˆq�E�L‰L˜ŒOØ“X�Ø�!•—‘˜A”Ø�!•—‘˜A˜a�CÖ ñ ð �6ˆMr0   )r   r   r   Úmpq_1_4Úisintr:   Ú_is_real_typeÚ_re)
r   rD   r   r<   ÚntyperQ   Úvr   r    rP   s
   f&f,   @@@r.   Úpcfvrd   §   sÈ   ü€ ð@ ×!Ñ! !Ó$�H€A€uØ�‰�A‹€AØ�‰€AØ�‰€AØ�„|˜Ÿ	™	 ! A¥#Ÿš÷	%ñ 	%ð �MŠM˜!˜RÑ* 6Ñ*ˆØ×Ñ˜Q×Ò C×$5Ñ$5°a×$8Ò$8Ø—‘˜“
ˆAØˆ÷	ð 	ð �}Š}˜Q  Ñ. vÑ.Ð.r0   c                ó  a aa€ S P                  V4      w  opS P                  S4      oV VV3R lpS P                  V4      pS P                  S4      '       d)   S P                  S4      '       d   S P	                  V4      pV# )a  
Gives the parabolic cylinder function `W(a,z)` defined in (DLMF 12.14).

**Examples**

Value at the origin::

    >>> from mpmath import *
    >>> mp.dps = 25; mp.pretty = True
    >>> a = mpf(0.25)
    >>> pcfw(a,0)
    0.9722833245718180765617104
    >>> power(2,-0.75)*sqrt(abs(gamma(0.25+0.5j*a)/gamma(0.75+0.5j*a)))
    0.9722833245718180765617104
    >>> diff(pcfw,(a,0),(0,1))
    -0.5142533944210078966003624
    >>> -power(2,-0.25)*sqrt(abs(gamma(0.75+0.5j*a)/gamma(0.25+0.5j*a)))
    -0.5142533944210078966003624

c               3   ó:  <"  € SP                  SP                  R SP                  S,          ,           4      4      p SP                  R SP                  S,          ,           4      SP                  R SP                  S,          ,
          4      ,
          R,          p SP                  ^,          R V ,          ,           pSP                  ^SP                  ^SP                  ,          S,          4      ,           4      SP                  SP                  S,          4      ,
          pSP                  V^,          4      SP                  RSP                  ,          S,          4      ,          pVSP                  V4      ,          SP                  SP                  S,          SSP                  R4      ,          4      ,          x € VSP                  V) 4      ,          SP                  SP                  ) S,          SSP                  R4      ,          4      ,          x € R# 5i)r   y               @rT   Nr
   )
ÚargÚgammaÚjÚloggammar   r   r   ÚexpjrF   rK   )Úphi2ÚrhoÚkÚCr   r   r   s       €€€r.   r*   Úpcfw.<locals>.terms  sW  øé € Ø�w‰w�s—y‘y  s§u¡u¨Q¥w¥Ó/Ó0ˆØ—‘˜S §¡ q¥�[Ó)¨C¯L©L¸¸S¿U¹UÀ1½W½Ó,EÕEÀrÕIˆØ�f‰f�Q�h˜˜T�Õ!ˆà�H‰H�Q˜Ÿ™  3§6¡6¥¨!¥Ó,Õ,Ó-°·±¸¿¹¸q½Ó0AÕAˆØ�H‰H�Q�q•S‹M˜CŸG™G D¨¯©¥K°¥MÓ2Õ2ˆØ�#—(‘(˜3“-Õ #§(¡(¨3¯5©5°­7°A°c·j±jÀÓ6GÕ4GÓ"HÕHÒHØ�#—(‘(˜C˜4“.Õ  3§8¡8¨S¯U©U¨F°1­H°a¸¿
¹
À4Ó8HÕ6HÓ#IÕIÔIùs   ƒHH)r   r   Úsum_accuratelyr`   ra   )r   rD   r   r<   rE   r*   rc   r   s   f&f,   @r.   Úpcfwrr   ð   sq   ú€ ð, ×Ñ˜aÓ �D€A€qØ�‰�A‹€A÷Jð 	×Ñ˜5Ó!€AØ
×Ñ˜×Ò × 1Ñ 1°!× 4Ò 4Ø�G‰G�A‹JˆØ€Hr0   c                 óT  aaa€ V P                  S4      '       d   ^ SS,           ,          # V P                  SR,           4      '       dF   V P                  S^,           4      '       d   \        R4      hVV3R lpV P                  ! VS.3/ VB # VV3R lpV P                  ! VS.3/ VB # )r3   r   z#Gegenbauer function with two limitsc           	      ó�   <€ ^V ,          p. . SV,           .S^,           V.S) SV,           .V R,           .R^S,
          ,          3pV.# ©é   r   © )rD   Úa2rO   r   r   s   &  €€r.   rQ   Úgegenbauer.<locals>.h=  sM   ø€ Ø�1•ˆBØ�B˜˜2�˜  1¥ b 	¨Q¨B°°"µ¨:¸¸#½°wÀÀQÀqÅSÅ	ÐIˆAØ�3ˆJr0   c           	      óŒ   <€ ^S,          p. . W,           .V ^,           V.V ) W,           .SR,           .R^S,
          ,          3pV.# ru   rw   )r   rx   rO   rD   r   s   &  €€r.   rQ   ry   B  sI   ø€ Øˆq�SˆØ��Q•T�F˜Q˜q�S "˜I¨¨¨A­D z°A°cµE°7¸CÀÀ1Å½IÐEˆØˆsˆ
r0   )r   ÚNotImplementedErrorr:   ©r   r   rD   r   r<   rQ   s   &fff, r.   Ú
gegenbauerr}   3  s‘   ú€ ð ‡{�{�1‡~‚~Ø�!�A•#�wˆØ
‡{�{�1�S•5×Òð �;‰;�q˜•s×ÒÜ%Ð&KÓLÐLö	ð �}Š}˜Q  Ñ. vÑ.Ð.öð �=Š=˜˜Q˜CÑ* 6Ñ*Ð*r0   c                 ó’  aaa€ V P                  S4      '       g   VVV3R  lpV P                  ! Wa.3/ VB # V P                  S4      '       g   VV3R lpV P                  ! WaS.3/ VB # V P                  VS,           V4      V P                  ! V) ^V,           S,           S,           S^,           ^S,
          ^,          3/ VB ,          # )c                 ó²   <€ . . SV ,           ^,           .V ^,           S^,           .V ) SS,           V ,           ^,           .S^,           .^S,
          R,          33# ©r   r   rw   ©r   rD   ÚbÚxs   &€€€r.   rQ   Újacobi.<locals>.hK  sQ   ø€ Ø˜˜a �c !�e˜W q¨¥s¨A¨a­C j°A°2°q¸µs¸1µu¸Qµw°-À!ÀAÅ#ÀÈÈ1ÍÈcÍ	ÐRÐTÐTr0   c                 óš   <€ . . S) .V ^,           S) V ,
          .V ) VS,           V ,           ^,           .S^,           .S^,           R,          33# r€   rw   r�   s   &&€€r.   rQ   r„   O  sM   ø€ Ø˜˜q˜b˜T A a¥C¨!¨¨A­ ;°!°°Q°qµS¸µU¸1µW°ÀÀ!Å¸uÀqÈÅsÈCÅiÐPÐRÐRr0   )r   r:   r_   ÚbinomialÚhyp2f1)r   r   rD   r‚   rƒ   r<   rQ   s   &&fff, r.   Újacobirˆ   H  sŸ   ú€ à�;‰;�q�>Š>÷	Uà�}Š}˜Q Ñ. vÑ.Ð.Ø�9‰9�Q�<Š<ö	Sà�}Š}˜Q A Ñ1¨&Ñ1Ð1à�<‰<˜˜!�˜AÓ §¢¨Q¨B¨q°­s°1­u°Q­w°q¸µs¸A¸a½CÀ½7Ñ!MÀfÑ!MÕMÐMr0   c                 ó<   aa€ VV3R  lpV P                   ! WR.3/ VB # )c                 ój   <€ . . V S,           ^,           .V ^,           S^,           .S) .V ^,           .S33# r@   rw   )rD   r   r   s   &€€r.   rQ   Úlaguerre.<locals>.hZ  s;   ø€ Ø�R˜!˜A�#˜a�%˜ 1 Q¥3¨¨!­ *°¨r¨d°Q°qµS°E¸1Ð=Ð?Ð?r0   r9   r|   s   &f&f, r.   ÚlaguerrerŒ   U  s   ù€ ö
@à�=Š=˜˜CÑ* 6Ñ*Ð*r0   c                 óˆ  € V P                  V4      '       d�   \        V4      pW^ 8  ,           ^,          '       d^   V'       g   V# V P                  V4      pVRV P                  ,          ^
,
          8  d   V# VR8  d   V ;P                  V) ,          un        V P                  ! V) V^,           ^^V,
          ^,          3/ VB # )r3   éþÿÿÿéûÿÿÿ)r_   ÚintÚmagr   r‡   )r   r   rƒ   r<   r‘   s   &&&, r.   Úlegendrer’   ^  s–   € à
‡y�y�‡|‚|Ü�‹Fˆà�Q‘�K˜1×ÔßØ�Ø—'‘'˜!“*ˆCØ�R˜Ÿ™•[ •^Ô#Ø�Ø�RŒxØ—’˜S˜DÕ •Ø�:Š:�q�b˜˜1�˜Q  !¥ Q�wÑ1¨&Ñ1Ð1r0   c                 ó  a€ V P                  V4      pV P                  V4      pV'       g   V P                  ! VS3/ VB # V^8X  d   V3R lpV P                  ! WaV.3/ VB # V^8X  d   V3R lpV P                  ! WaV.3/ VB # \        R4      h)rv   c           	      ó¢   <€ VR ,          p^S,           ^S,
          .W") .. ^V,
          .V ) V ^,           .^V,
          .R ^S,
          ,          3pV3# ©r   rw   ©r   ÚmÚgrO   r   s   &&  €r.   rQ   Úlegenp.<locals>.hw  óU   ø€ Ø�#•ˆAØ�1•�a˜•c�
˜Q ˜G R¨!¨A­#¨°!°°Q°qµS°	¸A¸a½C¸5À#ÀqÈÅsÅ)ÐKˆAØ�4ˆKr0   c           	      ó¢   <€ VR ,          pS^,           S^,
          .W") .. ^V,
          .V ) V ^,           .^V,
          .R ^S,
          ,          3pV3# r•   rw   r–   s   &&  €r.   rQ   r™   }  rš   r0   úrequires type=2 or type=3)r   r’   r:   Ú
ValueError©r   r   r—   r   Útyper<   rQ   s   &&&f&, r.   Úlegenpr    m  s�   ø€ ð 	�‰�A‹€AØ�‰�A‹€AçØ�|Š|˜A˜qÑ+ FÑ+Ð+àˆq„yõ	ð �}Š}˜Q 1 Ñ0¨Ñ0Ð0Øˆq„yõ	ð �}Š}˜Q 1 Ñ0¨Ñ0Ð0Ü
Ð0Ó
1Ð1r0   c                 óŒ  a a€ S P                  V4      pS P                  V4      pS P                  S4      oSR9   d   S P                  # V^8X  d   V V3R lpS P                  ! WaV.3/ VB # V^8X  dI   \        S4      ^8”  d   V V3R lpS P                  ! WaV.3/ VB # V V3R lpS P                  ! WaV.3/ VB # \	        R4      h)r   c                 óœ  <€ SP                  V4      w  r#^V,          SP                  ,          pTp^S,           p^S,
          pV^,          p^S,
          ^,          p	WEWg.R^Wˆ) .. ^V,
          .V ) V ^,           .^V,
          .V	3p
V) Wg.RV) V.W,           ^,           .W,
          ^,           V^,           .V ) V ^,           .V^,           .V	3pW«3# ©rv   éÿÿÿÿ)rV   r   )r   r—   ÚcosÚsinr\   r[   rD   r‚   r$   r%   r!   r+   r   r   s   &&          €€r.   rQ   Úlegenq.<locals>.h�  sÝ   ø€ Ø—‘ qÓ)‰HˆCØ�C•˜#Ÿ&™&Õ ˆAØˆAØ�!•ˆAØ�!•ˆAØ�!•ˆAØ�1•�a•ˆAØ˜�  A q¨"˜~¨r°A°aµC°5Ø��Q�q•S�	˜A˜a�C˜5 !ð$ˆBà�"�a�˜b 1 " a˜[¨1­3¨q­5¨'°AµC¸µE¸1¸Q½3°<Ø��Q�q•S�	˜A˜a�C˜5 !ð$ˆBà�6ˆMr0   c                 ón  <€ SP                  V4      ^SP                  SS^,
          S^,           .^V ) ^,
          RV ) V,
          ^,
          RV,          RV,          .W,           ^,           .V R,           .R^V ,           V,           ,          R^V ,           V,           ,          .V R,           .SR,          3pV.# )rv   r   g      ø?rŽ   )rK   r   )r   r—   r!   r   r   s   && €€r.   rQ   r§   ¢  s¡   ø€ Ø—j‘j “m Q¨¯©°°1°Qµ3¸¸!½Ð<Ø˜!˜˜A�˜s Q B q¥D¨¥F¨C°­E°3°qµ5Ð9Ø•c˜!•e�W˜q �u˜gØ˜1˜Q�3˜q�5•k 3¨¨!­¨A­¥;Ð/°!°Cµ%°¸!¸b½'ðB�ð �t�r0   c                 ó¶  <€ ^S
P                  V4      ,          S
P                  ,          pS
P                  V4      p^S,           pS^,
          pV^,          p^S,
          ^,          pW#WE.R^Wf) .. ^V,
          .V ) V ^,           .^V,
          .V3pV) W4V.R^V) V.W,           ^,           .W,
          ^,           V^,           .V ) V ^,           .V^,           .V3p	W‰3# r£   )Úsinpir   rK   )r   r—   r\   r[   rD   r‚   r$   r%   r!   r+   r   r   s   &&        €€r.   rQ   r§   «  sâ   ø€ Ø˜Ÿ	™	 !›Õ$ s§v¡vÕ-�Ø—J‘J˜q“M�Ø�a•C�Ø�a•C�Ø�a•C�Ø�q•S˜!•G�Ø˜A�\ B¨¨1¨b >°2¸¸!½°uØ�R˜˜1��I  !¥˜u að(�à�b˜! �] R¨¨Q¨B° N°QµS¸µU°G¸a½cÀ!½eÀQÀqÅS¸\Ø�R˜˜1��I  !¥˜u að(�à�v�r0   rœ   )r   r¤   )r   Únanr:   Úabsr�   rž   s   f&&f&, r.   Úlegenqr­   „  sÂ   ù€ ð 	�‰�A‹€AØ�‰�A‹€AØ�‰�A‹€AØˆG„|ð �w‰wˆØˆq„yö	ð �}Š}˜Q A Ñ1¨&Ñ1Ð1Øˆq„yô ˆq‹6�AŒ:öð —=’= ¨ FÑ5¨fÑ5Ð5öð —=’= ¨ FÑ5¨fÑ5Ð5Ü
Ð0Ó
1Ð1r0   c                 óè   € V'       gG   V P                  V4      '       d0   \        V P                  V4      4      ^,          ^8X  d
   V^ ,          # V P                  ! V) VR^V,
          ^,          3/ VB # )rv   )r   rv   ©r_   r�   ra   r‡   ©r   r   rƒ   r<   s   &&&,r.   Úchebytr±   º  sV   € ç�3—9‘9˜Q—<’<¤C¨¯©°«
£O°aÕ$7¸1Ô$<Ø�1�uˆØ�:Š:�q�b˜˜5 ! A¥# q¥Ñ3¨FÑ3Ð3r0   c                 ó  € V'       gG   V P                  V4      '       d0   \        V P                  V4      4      ^,          ^8X  d
   V^ ,          # V^,           V P                  ! V) V^,           R^V,
          ^,          3/ VB ,          # )rv   )é   rv   r¯   r°   s   &&&,r.   Úchebyur´   À  sc   € ç�3—9‘9˜Q—<’<¤C¨¯©°«
£O°aÕ$7¸1Ô$<Ø�1�uˆØˆa�C�3—:’:˜q˜b ! A¥# u¨q°­s°A­gÑ@¸Ñ@Õ@Ð@r0   c                 ó`  a aa€ S P                  V4      pS P                  V4      pS P                  S4      oS P                  S4      oS P                  V4      pT;'       d    V^ 8¬  pS P                  V4      pV'       d.   V^ 8  d'   V'       d   S P                  ! V^,           ) VSS3/ VB # S^ 8X  d#   V'       d   V^ 8  d   S P                  R,          # V'       d5   V'       d-   \	        V4      V8”  d   S P                  R,          # V VV3R lp	MV VV3R lp	S P
                  ! W‘V.3/ VB # )r3   rJ   c           
      óJ  <€ \        V4      pRSP                  VS,          4      ^V ,          ^,           SP                  W,           4      ,          SP                  ,          SP                  W,
          4      ,          SP	                  S4      ^,          SP                  V4      ^.pRV,          SP                  V4      ^,           ,          ^RRV,          RV) ^,
          .pW4. . W ,
          W,           ^,           .V^,           .SP	                  RS,          4      ^,          33# )r   r   r¤   )r¬   rk   Úfacr   r¦   Úsign)rX   r—   Úabsmro   ÚPr   ÚphiÚthetas   &&   €€€r.   rQ   Úspherharm.<locals>.hØ  sè   ø€ Ü�q“6ˆDØ�S—X‘X˜a �e“_Ø�A•#�a•%˜Ÿ™ ¥›Õ(¨¯©Õ/°·±¸½³Õ?Ø—‘˜“ Õ"Ø—‘˜“ ð#ˆAð �Q•˜Ÿ™ › A�Õ&¨¨3°°Dµ¸"¸t¸eÀA½gÐFˆAØ˜2˜r D¥F¨A­F°1­HÐ#5¸¸Q½°xØ—‘˜˜E�	Ó" AÕ%ð'ð )ð )r0   c                 ó°  <€ SP                  W,
          ^,           4      '       gC   SP                  W,           ^,           4      '       g   SP                  ^V,
          4      '       d   ^ .R.. . . . ^ 33# SP                  RS,          4      w  r#RSP                  VS,          4      ,          ^V ,          ^,           SP                  ,          SP	                  W,
          ^,           4      SP	                  W,           ^,           4      V^,          V^,          .p^RRRRV,          RV,          .pWE. ^V,
          .V ) V ^,           .^V,
          .V^,          33# )r   r   r¤   g      à¿)r   Úcos_sinrk   r   rh   )	rX   r—   r¥   r¦   ro   rº   r   r»   r¼   s	   &&    €€€r.   rQ   r½   ä  s  ø€ Ø�{‰{˜1�3˜q�5×!Ò! S§[¡[°µ°Qµ×%7Ò%7¸3¿;¹;ÀqÈÅs×;KÒ;KØ˜˜r˜d B¨¨B°°AÐ6Ð8Ð8Ø—{‘{ 3 u¥9Ó-‰HˆCØ�S—X‘X˜a �e“_Õ$ q¨¥s¨1¥u¨c¯f©f¥nØ—‘˜1�3˜q�5Ó! 3§9¡9¨Q­S°­UÓ#3Ø�a•˜˜a�ð!ˆAð �C˜˜d C¨¥E¨4°­6Ð2ˆAØ˜2  !¥˜u¨ r¨!¨A­# h°°1µ°°s¸AµvÐ>Ð@Ð@r0   )r   r_   Ú	spherharmÚzeror¬   r:   )
r   rX   r—   r¼   r»   r<   Úl_isintÚ	l_naturalÚm_isintrQ   s
   f&&ff,    r.   rÀ   rÀ   Æ  sô   ú€ à�‰�A‹€AØ�‰�A‹€AØ�K‰K˜Ó€EØ
�+‰+�cÓ
€CØ�i‰i˜‹l€GØ×"Ð"˜A ™F€IØ�i‰i˜‹l€Gß�1�q”5ŸWØ�}Š}˜q �s˜V Q¨¨sÑ=°fÑ=Ð=Ø�„z—g ! a¤%Ø�x‰x˜"�}Ðß—WÜˆq‹6�AŒ:Ø—8‘8˜b•=Ð ÷	)ð 	)÷	Að �=Š=˜˜q˜EÑ, VÑ,Ð,r0   N)rv   )Ú	functionsr   r   r/   r=   rB   rF   rd   rr   r}   rˆ   rŒ   r’   r    r­   r±   r´   rÀ   rw   r0   r.   Ú<module>rÆ      s:  ðß +ò7ðr ñMó ðMð ñ5Mó ð5Mðn ñ,'ó ð,'ð\ ñE/ó ðE/ðP ñ#ó ð#ðJð: ñ+ó ð+ð( ñ
Nó ð
Nð ñ+ó ð+ð ñ2ó ð2ð ó2ó ð2ð, ó32ó ð32ðj ñ4ó ð4ð
 ñAó ðAð
 ñ&-ó ò&-r0   