Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab27)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ab27.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(9/2), -(19/4)}, -z] == (1/(62214075 z^(1/4))) (Sqrt[2] (-9 (-6912675 - 13906200 z - 4767840 z^2 + 2145024 z^3 - 272384 z^4 + 16384 z^5) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (62214075 + 42203700 z - 29161440 z^2 + 5027904 z^3 - 393216 z^4 + 16384 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 12 z (20738025 - 13582800 z + 3123120 z^2 - 315392 z^3 + 16384 z^4) BesselJ[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]