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

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.agfg.01

Input Form

HypergeometricPFQ[{23/4}, {-(7/2), -(19/4)}, z] == -((1/(455095958625 z^(1/4))) (Sqrt[2] ((-455095958625 + 752790307500 z - 45258665760 z^2 - 171567063360 z^3 - 125189729280 z^4 + 588937789440 z^5 + 1208077516800 z^6 + 45059407872 z^7 + 67108864 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-455095958625 + 145995696000 z + 264982188240 z^2 + 116644872960 z^3 - 21033492480 z^4 + 543634882560 z^5 + 152690491392 z^6 + 1392508928 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-455095958625 - 460798915500 z - 233836439760 z^2 - 106128126720 z^3 - 124582993920 z^4 + 195052830720 z^5 + 10233053184 z^6 + 16777216 z^7) 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]