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

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=3, a₂>=3

For fixed z and a₁=3, a₂=5, b₁>=-11/2

For fixed z and a₁=3, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3, 5}, {-(9/2), 1}, z] == (1/45360) (45360 - 151200 z + 259200 z^2 - 403200 z^3 + 806400 z^4 - 4064256 z^5 - 5781285 z^6 - 2479290 z^7 - 472344 z^8 - 43952 z^9 - 1936 z^10 - 32 z^11) + (1/90720) (E^z Sqrt[Pi] (-12282075 z^(11/2) - 13662900 z^(13/2) - 5391516 z^(15/2) - 986784 z^(17/2) - 89808 z^(19/2) - 3904 z^(21/2) - 64 z^(23/2)) 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]