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

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`=11/2

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

Input Form

HypergeometricPFQ[{17/4}, {11/2, -(17/4)}, z] == -((1/(11032320 Sqrt[2] z^(15/4))) (7 (4 z (517517413875 + 143637486300 z + 15993780480 z^2 + 939950080 z^3 + 30146560 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (1552552241625 + 726636695400 z + 114697607040 z^2 + 8866974720 z^3 + 384040960 z^4 + 7602176 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (4657656724875 + 3067082795700 z + 713226895920 z^2 + 74083875840 z^3 + 4179148800 z^4 + 128450560 z^5 + 1048576 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2))

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]