Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7uj)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7uj.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(7/4)}, -z] == (1/(6083470008 Sqrt[2] z^(9/4))) ((4 z (-3738534345 + 1665004896 z + 3685665024 z^2 - 1769324544 z^3 + 1271070720 z^4 + 209977344 z^5 + 4194304 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-6230890575 - 1740693240 z + 3018152448 z^2 - 1299474432 z^3 + 546766848 z^4 + 103153664 z^5 + 2097152 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-93463358625 - 17802544500 z - 12957459840 z^2 + 22928126976 z^3 - 10114301952 z^4 + 4470865920 z^5 + 827326464 z^6 + 16777216 z^7) 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]