Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7440)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-17/4

http://functions.wolfram.com/07.22.03.7440.01

Input Form

HypergeometricPFQ[{5}, {-(17/4), -(3/4)}, z] == (1/716040) ((8 E^(2 Sqrt[z]) (89505 + 140400 z + 563175 z^2 - 199200 z^3 + 81056 z^4 + 512 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-1081575 + 2163150 Sqrt[z] - 1101240 z - 681720 z^(3/2) + 671232 z^2 + 335616 z^(5/2) + 47104 z^3 + 2048 z^(7/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] z^(7/4) (1081575 + 2163150 Sqrt[z] + 1101240 z - 681720 z^(3/2) - 671232 z^2 + 335616 z^(5/2) - 47104 z^3 + 2048 z^(7/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]