Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anuj)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.anuj.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(3/2), 3/2}, z] == (1/85050) (85050 - 1247400 z + 22702680 z^2 + 145945800 z^3 + 221621400 z^4 + 140687820 z^5 + 45242820 z^6 + 8034009 z^7 + 812940 z^8 + 46200 z^9 + 1360 z^10 + 16 z^11) + (1/170100) (E^z Sqrt[Pi] z^(5/2) (113513400 + 437837400 z + 552972420 z^2 + 320245380 z^3 + 97810335 z^4 + 16838010 z^5 + 1670760 z^6 + 93744 z^7 + 2736 z^8 + 32 z^9) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]