Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7r2)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a7r2.01

Input Form

HypergeometricPFQ[{-(17/4)}, {3/2, 13/4}, z] == ((-2 Sqrt[z] (1964187225 - 825153769440 z + 1737909169920 z^2 - 732507291648 z^3 + 75223203840 z^4 - 2212495360 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (3273645375 - 27935107200 z + 1194746192640 z^2 - 669843947520 z^3 + 73312043008 z^4 - 2197815296 z^5 + 16777216 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (9820936125 - 62853991200 z + 1256311330560 z^2 - 678217236480 z^3 + 73580347392 z^4 - 2199912448 z^5 + 16777216 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (809789460480 Sqrt[2] z^(7/4))

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]