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

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{9/4}, {11/2, -(17/4)}, z] == -((1/(282880 Sqrt[2] z^(15/4))) (21 (4 z (11500386975 + 2440898460 z + 169905600 z^2 + 3998720 z^3 + 16384 z^4) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (34501160925 + 13894345080 z + 1563131520 z^2 + 62648320 z^3 + 720896 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (103503482775 + 61397984340 z + 11604867120 z^2 + 746745600 z^3 + 16732160 z^4 + 65536 z^5) 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]