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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{1/4}, {5/2, 23/4}, z] == (1/(10485760 Sqrt[2] z^(17/4))) (209 (2 Sqrt[z] (-259875 - 158400 z + 23040 z^2 + 81920 z^3 + 65536 z^4) BesselI[-(1/4), Sqrt[z]]^2 + (779625 + 1663200 z - 184320 z^2 - 122880 z^3 - 65536 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (779625 + 69120 z^2 + 98304 z^3 + 65536 z^4) 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]