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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{21/4}, {11/2, -(23/4)}, z] == (1/(8158824960 z^(9/2))) (2 Sqrt[z] (795886079113125 + 547229452770000 z + 117840206484000 z^2 + 12791338560000 z^3 + 903930593280 z^4 + 58223493120 z^5 + 3030384640 z^6 + 33554432 z^7) Cosh[2 Sqrt[z]] - (795886079113125 + 1608410891587500 z + 564497759826000 z^2 + 83143700640000 z^3 + 7057290240000 z^4 + 454056345600 z^5 + 28966912000 z^6 + 889192448 z^7) Sinh[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]