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

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.abfi.01

Input Form

HypergeometricPFQ[{-(1/4)}, {11/2, -(19/4)}, z] == -((1/(1397792 Sqrt[2] z^(13/4))) (3 (4 z (2464997535 + 186117360 z + 3776768 z^2 + 196608 z^3) BesselI[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (12324987675 + 2026141260 z + 65312640 z^2 + 508928 z^3) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (61624938375 + 15608478600 z + 1039796160 z^2 + 5918720 z^3 - 786432 z^4) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]