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

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=5/4, b_1`>=-11/2

For fixed z and a₁=5/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{5/4}, {11/2, -(9/4)}, z] == -((1/(3328 Sqrt[2] z^(15/4))) (7 (-76 z (1673595 + 247940 z + 8128 z^2) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (95394915 + 32303040 z + 2211296 z^2 + 19968 z^3) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (286184745 + 151420500 z + 22261008 z^2 + 580352 z^3) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2))

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]