Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8357)

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/07.22.03.8357.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 3/4}, -z] == ((2 z (1059782931900 + 4958319625875 z + 2749083440400 z^2 + 371323031040 z^3 + 16096583680 z^4 + 240582656 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (62960643900 + 3710549252025 z + 2541408685200 z^2 + 361654571520 z^3 + 15947980800 z^4 + 239927296 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (47220482925 + 881449014600 z + 8781210449550 z^2 + 5324234176800 z^3 + 734781864960 z^4 + 32073695232 z^5 + 480641024 z^6 + 2097152 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(2098578982500 Sqrt[2] z^(3/4))

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]