Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.abz5)

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=3/4, b_1`>=-11/2

For fixed z and a₁=3/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.abz5.01

Input Form

HypergeometricPFQ[{3/4}, {-(9/2), 17/4}, z] == -((1/(5505024 Sqrt[2] z^(11/4))) (13 (-6 Sqrt[z] (-253477917 + 261654624 z + 33935104 z^2 + 786432 z^3) BesselI[1/4, Sqrt[z]]^2 + (-3802168755 + 6628583808 z + 1783127808 z^2 + 88276992 z^3 + 524288 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 6 Sqrt[z] (1267389585 + 494236512 z + 47993088 z^2 + 851968 z^3) 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]