Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae7f)

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`=-7/2

http://functions.wolfram.com/07.22.03.ae7f.01

Input Form

HypergeometricPFQ[{13/4}, {-(7/2), -(21/4)}, -z] == (1/(986792625 Sqrt[2])) (z^(1/4) ((986792625 - 2148120000 z + 1568127600 z^2 - 496454400 z^3 + 137871360 z^4 - 20643840 z^5 + 32505856 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 - 4 Sqrt[z] (-986792625 + 1358685900 z - 551350800 z^2 + 143354880 z^3 - 51609600 z^4 - 58195968 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 12 z (-328930875 + 189750600 z - 55373760 z^2 + 14100480 z^3 + 2506752 z^4 + 2621440 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]