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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=9/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {9/2, 21/4}, z] == (221 (2 Sqrt[z] (38513475 + 226472400 z + 136604160 z^2 + 94347264 z^3 - 34930688 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 - 3 (64189125 + 331808400 z + 174451200 z^2 + 65331200 z^3 - 34013184 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (192567375 + 341787600 z + 176140800 z^2 + 69181440 z^3 - 34144256 z^4 + 1048576 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (9492037632 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]