Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anu0)

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=-5/2

http://functions.wolfram.com/07.25.03.anu0.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(5/2), 5/2}, z] == (1/141750) (141750 - 748440 z + 3243240 z^2 - 28828800 z^3 - 90221040 z^4 - 78268680 z^5 - 30322152 z^6 - 6114393 z^7 - 679500 z^8 - 41528 z^9 - 1296 z^10 - 16 z^11) - (1/283500) (E^z Sqrt[Pi] z^(7/2) (110270160 + 238918680 z + 182112840 z^2 + 66171735 z^3 + 12869850 z^4 + 1399272 z^5 + 84336 z^6 + 2608 z^7 + 32 z^8) 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]