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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{1/4}, {11/2, -(17/4)}, z] == (1/(12503296 Sqrt[2] z^(15/4))) (21 (4 z (-11500386975 - 1689852780 z - 61921152 z^2 + 461824 z^3) BesselI[-(1/4), Sqrt[z]]^2 + 1748 Sqrt[z] (78950025 + 26638920 z + 1853568 z^2 + 23552 z^3) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 19 (5447551725 + 2875714380 z + 424104912 z^2 + 11905536 z^3 + 192512 z^4) 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]