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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=9/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {9/2, 23/4}, -z] == (133 (2 Sqrt[z] (-34459425 - 162779760 z + 102366720 z^2 - 30941184 z^3 + 18546688 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + (103378275 + 330810480 z - 140659200 z^2 + 40771584 z^3 - 17891328 z^4 - 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (103378275 - 215051760 z + 115416576 z^2 - 35168256 z^3 + 18284544 z^4 + 1048576 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2085617664 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]