Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0584)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=2

http://functions.wolfram.com/07.22.03.0584.01

Input Form

HypergeometricPFQ[{-(11/2)}, {2, 6}, -z] == (1/(123867538970175 z^4)) (32 (2 z (-101140439400 - 63212774625 z - 50570219700 z^2 + 2595937944600 z^3 + 2768759476560 z^4 + 541202872896 z^5 + 32534046720 z^6 + 725326848 z^7 + 6156288 z^8 + 16384 z^9) BesselJ[0, Sqrt[z]]^2 - 16 Sqrt[z] (-50570219700 - 25285109850 z - 21070924875 z^2 + 147496474125 z^3 + 301393794240 z^4 + 64745758728 z^5 + 4000034304 z^6 + 90092160 z^7 + 768000 z^8 + 2048 z^9) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (-809123515200 - 303421318200 z - 282350393325 z^2 - 573129156600 z^3 + 3070153270800 z^4 + 5040971294688 z^5 + 1050922551168 z^6 + 64351899648 z^7 + 1444521984 z^8 + 12296192 z^9 + 32768 z^10) BesselJ[1, Sqrt[z]]^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]