Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8hy)

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`=-5/2

http://functions.wolfram.com/07.22.03.a8hy.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(5/2), 21/4}, z] == -((17 (2 Sqrt[z] (-2798273553075 + 3444028988400 z - 325361836800 z^2 + 9336729600 z^3 + 66375843840 z^4 + 13787725824 z^5 + 1459617792 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 (-4663789255125 + 9056520673200 z + 364799635200 z^2 + 116633088000 z^3 + 82354176000 z^4 + 15461253120 z^5 + 1694498816 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (-13991367765375 - 2678689213200 z - 71833132800 z^2 + 83566080000 z^3 + 78962688000 z^4 + 15146680320 z^5 + 1660944384 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(1743991603200 Sqrt[2] z^(15/4)))

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]