Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8567)

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`=-11/2

http://functions.wolfram.com/07.22.03.8567.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 21/4}, -z] == -(((2 Sqrt[z] (42271993507217599125 + 50248365720611058000 z + 2439364404135859200 z^2 + 232255092245299200 z^3 - 466996943418163200 z^4 + 68361159243202560 z^5 - 4481889305886720 z^6 + 171279000797184 z^7 - 4239132721152 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]]^2 - 3 (70453322512029331875 + 133847416654017066000 z - 11745087871765248000 z^2 + 792720570997555200 z^3 - 534957234300518400 z^4 + 72568431968256000 z^5 - 4638468042915840 z^6 + 175089710530560 z^7 - 4299262263296 z^8 + 68719476736 z^9) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (211359967536087995625 - 49359014114936526000 z + 1355202446742144000 z^2 + 669785295281356800 z^3 - 523325001056256000 z^4 + 71905616068608000 z^5 - 4614728617820160 z^6 + 174525996072960 z^7 - 4290672328704 z^8 + 68719476736 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (734820398058700800 Sqrt[2] z^(15/4)))

Standard Form

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MathML Form

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</math>

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]