Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aey0)

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aey0.01

Input Form

HypergeometricPFQ[{15/4}, {9/2, -(23/4)}, z] == (1/(26650008 Sqrt[2] z^(9/4))) ((-4 z (110924889075 + 25835838336 z + 2673151488 z^2 + 162054144 z^3 + 3866624 z^4) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (554624445375 + 178545767400 z + 23079200256 z^2 + 1702342656 z^3 + 65863680 z^4 + 524288 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 13 (213317094375 + 87632968500 z + 14311987200 z^2 + 1267402752 z^3 + 66060288 z^4 + 1310720 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^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]