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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(7/2), -(15/4)}, z] == (1/(23952418875 z^(1/4))) (Sqrt[2] ((23952418875 - 37411397100 z + 132723360 z^2 + 9366477120 z^3 + 27235676160 z^4 + 407726161920 z^5 + 73666658304 z^6 + 675282944 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (23952418875 - 5474838600 z - 13250215440 z^2 - 5435337600 z^3 + 22651453440 z^4 + 104968028160 z^5 + 4872732672 z^6 + 8388608 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 20 z (4790483775 + 5292343980 z + 3189784752 z^2 + 2116832256 z^3 + 6795436032 z^4 + 2976645120 z^5 + 32505856 z^6) 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]