Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8105)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8105.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), -(9/4)}, -z] == (1/(455625 Sqrt[2])) (z^(1/4) ((455625 - 445500 z + 205200 z^2 + 5184000 z^3 + 19514880 z^4 + 4259840 z^5 + 131072 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-455625 + 81000 z - 172800 z^2 + 2134080 z^3 + 522240 z^4 + 16384 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 4 z (455625 + 283500 z + 432000 z^2 + 4625280 z^3 + 1056768 z^4 + 32768 z^5) BesselJ[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]