Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8647)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.8647.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 5/4}, -z] == (1/(838252800 Sqrt[2] z^(1/4))) ((2 (838252800 + 236413485 z - 609828912 z^2 + 215373312 z^3 - 39739392 z^4 + 23396352 z^5 + 1048576 z^6) BesselJ[1/4, Sqrt[z]]^2 - 3 Sqrt[z] (1511692875 - 934884720 z + 277820928 z^2 - 58662912 z^3 + 22478848 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 z (1182067425 - 855716400 z + 265047552 z^2 - 56254464 z^3 + 22609920 z^4 + 1048576 z^5) 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]