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Special Functions
Two decades of intense R&D at Wolfram Research have given Mathematica by far the world's broadest and deepest coverage of special functions—and greatly expanded the whole domain of practical closed-form solutions. Often using original results and methods, all special functions in Mathematica support arbitrary-precision evaluation for all complex values of parameters, arbitrary series expansion even at branch points, and an immense web of exact relations, transformations and simplifications.
Gamma  ▪ Pochhammer  ▪ Beta  ▪ PolyGamma  ▪ LogGamma  ▪ ...
Erf  ▪ Erfc  ▪ ExpIntegralE  ▪ ExpIntegralEi  ▪ LogIntegral  ▪ FresnelS  ▪ SinIntegral  ▪ ...
Orthogonal Polynomials
LegendreP  ▪ HermiteH  ▪ LaguerreL  ▪ JacobiP  ▪ GegenbauerC  ▪ ChebyshevT  ▪ ChebyshevU  ▪ ZernikeR  ▪ SphericalHarmonicY
BesselJ  ▪ BesselY  ▪ BesselI  ▪ BesselK  ▪ AiryAi  ▪ AiryAiPrime  ▪ SphericalBesselJ  ▪ KelvinBer  ▪ HankelH1  ▪ StruveH  ▪ ...
Legendre-Related Functions
EllipticK  ▪ EllipticF  ▪ EllipticE  ▪ EllipticPi  ▪ ...
Modular Forms
Zeta  ▪ PolyLog  ▪ LerchPhi  ▪ RiemannSiegelZ  ▪ ...
    
N numerical evaluation to any precision
FunctionExpand expand in terms of simpler functions
FullSimplify apply full symbolic simplification
    
Derivative (') symbolic and numerical derivatives for arguments and parameters
FindRoot find numerical zeros of functions
TUTORIALS
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