Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9034)

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`=9/2

http://functions.wolfram.com/07.22.03.9034.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 9/4}, z] == ((2 z (677334457800 + 404800876414935 z - 608218297727040 z^2 + 178680457992960 z^3 - 15227567308800 z^4 + 457039478784 z^5 - 5020581888 z^6 + 16777216 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (2257781526000 + 63003441726225 z - 471699303435360 z^2 + 165999493820160 z^3 - 14834961039360 z^4 + 452671242240 z^5 - 5005901824 z^6 + 16777216 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 (-4233340361250 + 10160016867000 z + 87861712813875 z^2 - 487934353146240 z^3 + 167694950142720 z^4 - 14889679257600 z^5 + 453290557440 z^6 - 5007998976 z^7 + 16777216 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(365373208680480 Sqrt[2] z^(9/4))

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]