Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9zc)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a9zc.01

Input Form

HypergeometricPFQ[{-(7/4)}, {3/2, 23/4}, z] == (19 (2 Sqrt[z] (638512875 + 389188800 z - 78624000 z^2 + 1170800640 z^4 - 432013312 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (1915538625 + 4086482400 z - 518918400 z^2 + 201277440 z^3 + 928972800 z^4 - 421527552 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (1915538625 + 103783680 z^2 - 154828800 z^3 - 1069350912 z^4 + 427819008 z^5 - 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(29444014080 Sqrt[2] z^(17/4))

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]