Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag8u)

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`=7/2

http://functions.wolfram.com/07.22.03.ag8u.01

Input Form

HypergeometricPFQ[{21/4}, {7/2, -(17/4)}, z] == (1/(105496560 Sqrt[2] z^(7/4))) ((4 z (286184745 + 185870400 z + 125898240 z^2 - 1081344 z^3 - 1245184 z^4) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (858554235 + 642022920 z + 435517440 z^2 + 84086784 z^3 - 12648448 z^4 + 524288 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (2575662705 + 2416671180 z + 1331447040 z^2 + 577628160 z^3 - 17891328 z^4 - 4456448 z^5) 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]