Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad9u)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ad9u.01

Input Form

HypergeometricPFQ[{9/4}, {-(11/2), 19/4}, z] == (1/(62914560 Sqrt[2] z^(13/4))) ((2 Sqrt[z] (4745120254875 + 5143184046000 z + 868260556800 z^2 + 52805550080 z^3 + 1135083520 z^4 + 4194304 z^5) BesselI[-(1/4), Sqrt[z]]^2 - (14235360764625 + 37121530446000 z + 10791238348800 z^2 + 1024613990400 z^3 + 37106483200 z^4 + 390070272 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (14235360764625 + 6752760814800 z + 1012970649600 z^2 + 57759744000 z^3 + 1184890880 z^4 + 4194304 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]