Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ai3j)

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=2, a₂>=2

For fixed z and a₁=2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=2, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ai3j.01

Input Form

HypergeometricPFQ[{2, 9/2}, {-(11/2), 11/2}, -z] == (1/(1155 z^4)) (812851200 + 270950400 z + 81285120 z^2 + 19353600 z^3 + 3764355 z^4 + 616140 z^5 + 86940 z^6 + 10784 z^7 + 1200 z^8 + 128 z^9 + 32 z^10) - (1/(1155 z^(9/2))) ((16 Sqrt[Pi] (25401600 + 25401600 z + 12700800 z^2 + 4233600 z^3 + 1058400 z^4 + 211680 z^5 + 35280 z^6 + 5040 z^7 + 630 z^8 + 70 z^9 + 7 z^10 + 2 z^11) 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]