Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8265)

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`=1/2

http://functions.wolfram.com/07.22.03.8265.01

Input Form

HypergeometricPFQ[{-(23/4)}, {1/2, 7/4}, -z] == ((2 Sqrt[z] (2302888913325 + 22092626556000 z + 18577413953280 z^2 + 3368959426560 z^3 + 183268737024 z^4 + 3294625792 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (-316234143225 + 14465239588800 z + 16743940012800 z^2 + 3259755233280 z^3 + 181237776384 z^4 + 3284140032 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (316234143225 + 18482796652320 z + 17801011388160 z^2 + 3324398321664 z^3 + 182451634176 z^4 + 3290431488 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (4816600588800 Sqrt[2] z^(1/4))

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]