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

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`=-7/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(7/2), -(23/4)}, z] == (1 + (52 z)/23 + (1648 z^2)/1311 + (2816 z^3)/6555 + (8192 z^4)/45885 - (25296896 z^5)/195568425 + (4600102912 z^6)/45176306175 + (486539264 z^7)/316234143225) Cosh[2 Sqrt[z]] + (1/1581170716125) (2 Sqrt[z] (-1581170716125 - 1466593128000 z - 594356162400 z^2 - 194075481600 z^3 - 61785292800 z^4 + 128294584320 z^5 + 15487467520 z^6 + 33554432 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]