Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8958)

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`=7/2

http://functions.wolfram.com/07.22.03.8958.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(19/4)}, z] == ((-8 z (-883980264195 + 3753792246960 z + 991254087936 z^2 + 109403320320 z^3 + 7113867264 z^4 + 330301440 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (6324353933625 + 4877329781520 z + 1100856234240 z^2 + 116225593344 z^3 + 7427653632 z^4 + 344981504 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-94865309004375 + 29659039137000 z + 37126925216640 z^2 + 8653677742080 z^3 + 920915509248 z^4 + 59024867328 z^5 + 2743074816 z^6 + 134217728 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (11125145777130 Sqrt[2] z^(5/4))

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]