Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa06)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.aa06.01

Input Form

HypergeometricPFQ[{-(7/4)}, {5/2, 5/4}, z] == (1/(12480 z^(3/2))) ((-4 (21 + 42 Sqrt[z] - 504 z - 167 z^(3/2) + 716 z^2 + 16 z^(5/2) - 64 z^3 + E^(4 Sqrt[z]) (-21 + 42 Sqrt[z] + 504 z - 167 z^(3/2) - 716 z^2 + 16 z^(5/2) + 64 z^3)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (2457 - 2912 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (2457 - 2912 z + 256 z^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]