Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae53)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ae53.01

Input Form

HypergeometricPFQ[{13/4}, {-(11/2), -(9/4)}, -z] == -((1/(21049875 Sqrt[2])) (z^(1/4) ((-21049875 + 47628000 z - 38404800 z^2 + 19353600 z^3 - 161280 z^4 - 3522560 z^5 + 131072 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + 28 Sqrt[z] (-3007125 + 4398300 z - 2181600 z^2 + 838080 z^3 + 583680 z^4 + 114688 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (21049875 - 13948200 z + 5609520 z^2 + 1088640 z^3 - 688128 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]