Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj6s)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-5/2

http://functions.wolfram.com/07.25.03.aj6s.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(5/2), -(3/2)}, -z] == (1/405) (405 - 1080 z + 12600 z^2 + 453600 z^3 - 3350160 z^4 + 4612608 z^5 - 2351232 z^6 + 546240 z^7 - 61712 z^8 + 3264 z^9 - 64 z^10) + ((8/405) Sqrt[Pi] (-154440 z^(7/2) + 617760 z^(9/2) - 697320 z^(11/2) + 324660 z^(13/2) - 71943 z^(15/2) + 7914 z^(17/2) - 412 z^(19/2) + 8 z^(21/2)) Erfi[Sqrt[z]])/E^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]