Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8q2)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8q2.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, -(23/4)}, z] == ((-4 z (-4326070673925 + 144174192624 z + 191557545984 z^2 + 18323472384 z^3 + 638582784 z^4 + 8388608 z^5) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-7210117789875 - 138572834400 z + 104294227968 z^2 + 9447309312 z^3 + 322961408 z^4 + 4194304 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (108151766848125 + 11692082902500 z + 1436118465600 z^2 + 823816175616 z^3 + 75242668032 z^4 + 2579496960 z^5 + 33554432 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(314443444392 Sqrt[2] z^(9/4))

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]