Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a84p)

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`=-1/2

http://functions.wolfram.com/07.22.03.a84p.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(1/2), 23/4}, -z] == -((19 (2 Sqrt[z] (37611600901875 - 26746027308000 z - 3969725760000 z^2 - 846874828800 z^3 - 2860705382400 z^4 + 4327420723200 z^5 + 4017975459840 z^6 + 308700774400 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + (-112834802705625 + 252176828904000 z + 11115232128000 z^2 + 5081248972800 z^3 + 1737179136000 z^4 - 2284742246400 z^5 - 3832251678720 z^6 - 306016419840 z^7 - 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-112834802705625 + 11462583132000 z - 1111523212800 z^2 - 1498317004800 z^3 - 2861236224000 z^4 + 3435606835200 z^5 + 3942477987840 z^6 + 307627032576 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(120131577446400 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]