Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9050)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9050.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(23/4)}, z] == ((-4 z (6648673127695223625 - 329473542526128000 z + 34867150084166400 z^2 + 55621894899916800 z^3 + 7395200999424000 z^4 + 440280457150464 z^5 + 15111423000576 z^6 + 326954385408 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (11081121879492039375 + 435866040633523500 z + 49546610345232000 z^2 + 31435766201548800 z^3 + 3902605185024000 z^4 + 227006931271680 z^5 + 7701924937728 z^6 + 165356240896 z^7 + 2147483648 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-166216828192380590625 - 21312819782158905000 z - 819231511146048000 z^2 + 342903227022720000 z^3 + 246627237865881600 z^4 + 30965503603507200 z^5 + 1807795271761920 z^6 + 61443466592256 z^7 + 1320702443520 z^8 + 17179869184 z^9) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(88704495662983200 Sqrt[2] z^(13/4))

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]