+
    ‹°³j½  ã                   óV  € R t ^ RIHtHtHtHtHtHtHtH	t	 ^ RI
HtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtHtH t H!t!H"t" ^ RI#H$t$H%t%H&t&H't'H(t(H)t)H*t*H+t+ ^ RI,H-t-H.t.H/t/H0t0H1t1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9H:t: ^ RI;H<t<H=t=H>t>H?t?H@t@HAtAHBtBHCtCHDtDHEtEHFtFHGtGHHtHHItI ^ RIJHKtKHLtLHMtMHNtN ^ RIOHPtPHQtQHRtRHStSHTtTHUtUHVtVHWtWHXtXHYtYHZtZH[t[ ^ RI\H]t]H^t^H_t_ ^ R	I`HataHbtbHctc ^ R
IdHeteHftfHgtgHhthHitiHjtjHktkHltlHmtmHntnHotoHptpHqtqHrtrHstsHtttHutuHvtv ^ RIwHxtxHytyHztzH{t{H|t|H}t}H~t~Ht ^ RI€H�t�H‚t‚HƒtƒH„t„H…t…H†t† ^ RI‡HˆtˆH‰t‰HŠtŠ ^ RI‹HŒtŒ ^ RI�HŽtŽH�t� ^ RI�H‘t‘H’t’H“t“ ^ RI”H•t•H–t–H—t—H˜t˜H™t™HštšH›t›HœtœH�t�HžtžHŸtŸH t H¡t¡H¢t¢H£t£H¤t¤ ^ RI¥H¦t¦H§t§H¨t¨ ^ RI©HªtªH«t«H¬t¬H­t­H®t®H¯t¯H°t°H±t±H²t²H³t³H´t´HµtµH¶t¶ ^ RI·H¸t¸H¹t¹Hºtº ^ RI»H¼t¼H½t½H¾t¾H¿t¿ ^ RIÀHÁtÁHÂtÂHÃtÃ ^ RIÄHÅtÅHÆtÆHÇtÇHÈtÈ ]MtÉ. RNRNRNRNRNRNRNRNR NR!NR"NR#NR$NR%NR&NR'NR(NR)NR*NR+NR,NR-NR.NR/NR0NR1NR2NR3NR4NR5NR6NR7NR8NR9NR:NR;NR<NR=NR>NR?NR@NRANRBNRCNRDNRENRFNRGNRHNRINRJNRKNRLNRMNRNNRONRPNRQNRRNRSNRTNRUNRVNRWNRXNRYNRZNR[NR\NR]NR^NR_NR`NRaNRbNRcNRdNReNRfNRgNRhNRiNRjNRkNRlNRmNRnNRoNRpNRqNRrNRsNRtNRuNRvNRwNRxNRyNRzNR{NR|NR}NR~NRNR€NR�NR‚NRƒNR„NR…NR†NR‡NRˆNR‰NRŠNR‹NRŒNR�NRŽNR�NR�NR‘NR’NR“NR”NR•NR–NR—NR˜NR™NRšNR›NRœNR�NRžNRŸNR NR¡NR¢NR£NR¤NR¥NR¦NR§NR¨NR©NRªNR«NR¬NR­NR®NR¯NR°NR±NR²NR³NR´NRµNR¶NR·NR¸NR¹NRºNR»NR¼NR½NR¾NR¿NRÀNRÁNRÂNRÃNRÄNRÅNRÆNRÇNRÈNRÉNtÊRÊ# )ËzôA functions module, includes all the standard functions.

Combinatorial - factorial, fibonacci, harmonic, bernoulli...
Elementary - hyperbolic, trigonometric, exponential, floor and ceiling, sqrt...
Special - gamma, zeta,spherical harmonics...
)Ú	factorialÚ
factorial2ÚrfÚffÚbinomialÚRisingFactorialÚFallingFactorialÚsubfactorial)Ú
carmichaelÚ	fibonacciÚlucasÚ
tribonacciÚharmonicÚ	bernoulliÚbellÚeulerÚcatalanÚgenocchiÚandreÚ	partitionÚdivisor_sigmaÚudivisor_sigmaÚlegendre_symbolÚjacobi_symbolÚkronecker_symbolÚmobiusÚprimenuÚ
primeomegaÚtotientÚreduced_totientÚprimepiÚmotzkin)ÚsqrtÚrootÚMinÚMaxÚIdÚ	real_rootÚcbrtÚRem)ÚreÚimÚsignÚAbsÚ	conjugateÚargÚ
polar_liftÚperiodic_argumentÚunbranched_argumentÚprincipal_branchÚ	transposeÚadjointÚpolarifyÚ
unpolarify)ÚsinÚcosÚtanÚsecÚcscÚcotÚsincÚasinÚacosÚatanÚasecÚacscÚacotÚatan2)Ú	exp_polarÚexpÚlogÚLambertW)ÚsinhÚcoshÚtanhÚcothÚsechÚcschÚasinhÚacoshÚatanhÚacothÚasechÚacsch)ÚfloorÚceilingÚfrac)Ú	PiecewiseÚpiecewise_foldÚpiecewise_exclusive)ÚerfÚerfcÚerfiÚerf2ÚerfinvÚerfcinvÚerf2invÚEiÚexpintÚE1ÚliÚLiÚSiÚCiÚShiÚChiÚfresnelsÚfresnelc)ÚgammaÚ
lowergammaÚ
uppergammaÚ	polygammaÚloggammaÚdigammaÚtrigammaÚ
multigamma)Údirichlet_etaÚzetaÚlerchphiÚpolylogÚ	stieltjesÚ
riemann_xi)ÚEijkÚ
LeviCivitaÚKroneckerDelta)ÚSingularityFunction)Ú
DiracDeltaÚ	Heaviside)Úbspline_basisÚbspline_basis_setÚinterpolating_spline)ÚbesseljÚbesselyÚbesseliÚbesselkÚhankel1Úhankel2ÚjnÚynÚjn_zerosÚhn1Úhn2ÚairyaiÚairybiÚairyaiprimeÚairybiprimeÚmarcumq)ÚhyperÚmeijergÚappellf1)ÚlegendreÚassoc_legendreÚhermiteÚhermite_probÚ
chebyshevtÚ
chebyshevuÚchebyshevu_rootÚchebyshevt_rootÚlaguerreÚassoc_laguerreÚ
gegenbauerÚjacobiÚjacobi_normalized)ÚYnmÚYnm_cÚZnm)Ú
elliptic_kÚ
elliptic_fÚ
elliptic_eÚelliptic_pi)ÚbetaÚbetaincÚbetainc_regularized)ÚmathieusÚmathieucÚmathieusprimeÚmathieucprimer   r   r   r   r   r   r   r	   r
   r   r   r!   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   ÚlnrH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r€   r�   r‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r�   rŽ   r�   r�   r‘   r’   r“   r”   r•   r–   r—   r˜   r™   rš   r›   rœ   r�   rž   rŸ   r    r¡   r¢   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   N)ËÚ__doc__Ú(sympy.functions.combinatorial.factorialsr   r   r   r   r   r   r   r	   Ú%sympy.functions.combinatorial.numbersr
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   Ú(sympy.functions.elementary.miscellaneousr"   r#   r$   r%   r&   r'   r(   r)   Ú$sympy.functions.elementary.complexesr*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   Ú(sympy.functions.elementary.trigonometricr8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   Ú&sympy.functions.elementary.exponentialrF   rG   rH   rI   Ú%sympy.functions.elementary.hyperbolicrJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   Ú#sympy.functions.elementary.integersrV   rW   rX   Ú$sympy.functions.elementary.piecewiserY   rZ   r[   Ú'sympy.functions.special.error_functionsr\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   Ú'sympy.functions.special.gamma_functionsrn   ro   rp   rq   rr   rs   rt   ru   Ú&sympy.functions.special.zeta_functionsrv   rw   rx   ry   rz   r{   Ú(sympy.functions.special.tensor_functionsr|   r}   r~   Ú-sympy.functions.special.singularity_functionsr   Ú'sympy.functions.special.delta_functionsr€   r�   Ú sympy.functions.special.bsplinesr‚   rƒ   r„   Úsympy.functions.special.besselr…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r�   rŽ   r�   r�   r‘   r’   r“   r”   Úsympy.functions.special.hyperr•   r–   r—   Ú#sympy.functions.special.polynomialsr˜   r™   rš   r›   rœ   r�   rž   rŸ   r    r¡   r¢   r£   r¤   Ú+sympy.functions.special.spherical_harmonicsr¥   r¦   r§   Ú*sympy.functions.special.elliptic_integralsr¨   r©   rª   r«   Ú&sympy.functions.special.beta_functionsr¬   r­   r®   Ú)sympy.functions.special.mathieu_functionsr¯   r°   r±   r²   r³   Ú__all__© ó    ÚY/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/functions/__init__.pyÚ<module>rÐ      sô  ðñ÷K÷ Kó K÷I÷ I÷ I÷ I÷ I÷ Ió I÷"÷ "ó "÷D÷ D÷ D÷ D÷H÷ H÷ H÷ H÷ó ÷>÷ >÷ >ó >ç DÑ D÷Gñ G÷÷ ÷ ÷ ÷ ÷H÷ Hó H÷2÷ 2÷ñ å Mß Iß cÑ c÷i÷ i÷ i÷ ió iç BÑ B÷Z÷ Z÷ Zõ Z÷ HÑ G÷-ó -ç UÑ U÷&ó &à€ð=Øð=Øð=Ø#ð=Ø%)ð=Ø+5ð=Ø7Hð=àð=à&ð=ð ð	=ð ð	=ð  'ð	=ð )2ð	=ð 4@ð	=ð BLð	=ð
 ð=ð
 ð=ð
 !ð=ð
 #,ð=ð
 .8ð=ð
 :Að=ð
 CNð=ð ð=ð &ð=ð (9ð=ð ;Jð=ð L^ð=ð ð=ð ð=ð &ð=ð (1ð=ð 3Dð=ð FOð=ð ð=ð ð=ð ð=ð !ð=ð #'ð=ð )4ð=ð 6<ð=ð >Cð=ð 	ð=ð ð=ð ð=ð ð=ð  +ð=ð -2ð=ð 4@ð=ð ð=ð /ð=ð 1Cð=ð ð=ð ð=ð 'ð=ð )5ð=ð 
ð=ð ð=ð ð=ð ð=ð !&ð=ð (-ð=ð /5ð=ð 7=ð=ð ?Eð=ð GMð=ð  ð!=ð  ð!=ð  ð!=ð  $ð!=ð$ ð%=ð$ ð%=ð$ ð%=ð$ $ð%=ð$ &0ð%=ð( ð)=ð( ð)=ð( ð)=ð( #ð)=ð( %+ð)=ð( -3ð)=ð( 5<ð)=ð( >Eð)=ð( GNð)=ð* ð+=ð* ð+=ð* ð+=ð. ð/=ð. ð/=ð. ð/=ð2 ð3=ð2 "ð3=ð2 $9ð3=ð6 
ð7=ð6 ð7=ð6 ð7=ð6 "ð7=ð6 $,ð7=ð6 .7ð7=ð6 9Bð7=ð6 DHð7=ð8 ð9=ð8 ð9=ð8 ð9=ð8 ð9=ð8 !%ð9=ð8 '+ð9=ð8 -2ð9=ð8 49ð9=ð8 ;Eð9=ð: ð;=ð> ð?=ð> ð?=ð> (ð?=ð> *5ð?=ð> 7Að?=ð> CLð?=ð@ ðA=ð@ ðA=ðD ðE=ðD ðE=ðD (ðE=ðD *3ðE=ðD 5@ðE=ðD BNðE=ðH ðI=ðH ðI=ðH +ðI=ðL ðM=ðP ðQ=ðP ðQ=ðT ðU=ðT )ðU=ðT +AðU=ðX ðY=ðX ðY=ðX $ðY=ðX &/ðY=ðX 1:ðY=ðX <EðY=ðX GKðY=ðZ 	ð[=ðZ ð[=ðZ ð[=ðZ #ð[=ðZ %-ð[=ðZ /7ð[=ðZ 9Fð[=ð\ ð]=ð\ ð]=ð` ða=ð` ða=ð` #ða=ðd ðe=ðd !ðe=ðd #,ðe=ðd .<ðe=ðd >Jðe=ðf ðg=ðf $ðg=ðf &7ðg=ðf 9Cðg=ðh ði=ðh #ði=ðh %-ði=ðh /Bði=ðl 
ðm=ðl ðm=ðl ðm=ðp ðq=ðp ðq=ðp !-ðq=ðp /<ðq=ðt ðu=ðt ðu=ðt -ðu=ðx ðy=ðx ðy=ðx ,ðy=ðx .=ðy=‚rÎ   