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

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=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), 3/2}, z] == (1/13395375) (13395375 - 65488500 z + 170270100 z^2 - 389188800 z^3 + 1102701600 z^4 - 7618665600 z^5 - 18460612800 z^6 - 13830808320 z^7 - 4965060240 z^8 - 986821920 z^9 - 115406700 z^10 - 8069280 z^11 - 329088 z^12 - 7168 z^13 - 64 z^14) - (1/13395375) (2 E^z Sqrt[Pi] z^(11/2) (6666332400 + 11867536800 z + 7966633500 z^2 + 2704741200 z^3 + 520435125 z^4 + 59642730 z^5 + 4115160 z^6 + 166320 z^7 + 3600 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]