Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8842)

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`=1/2

http://functions.wolfram.com/07.22.03.8842.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 9/4}, z] == ((2 Sqrt[z] (902763556695 - 5780102328000 z + 6516893940480 z^2 - 1675208392704 z^3 + 120968773632 z^4 - 2730491904 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (13749310575 + 1930726717920 z - 5213019651840 z^2 + 1573282529280 z^3 - 118604365824 z^4 + 2715811840 z^5 - 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (41247931725 + 2236123169280 z - 5371739493120 z^2 + 1587119063040 z^3 - 118937419776 z^4 + 2717908992 z^5 - 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (911013143040 Sqrt[2] z^(3/4))

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]