Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0559)

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=3/2

http://functions.wolfram.com/07.22.03.0559.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3/2, 9/2}, z] == (1/(1274019840 z^(7/2))) (-2 Sqrt[z] (7016625 - 7952175 z + 26195400 z^2 - 204883830 z^3 + 75388770 z^4 - 6881994 z^5 + 212664 z^6 - 2372 z^7 + 8 z^8) Cosh[2 Sqrt[z]] + (7016625 + 1403325 z + 13097700 z^2 + 156486330 z^3 - 69536070 z^4 + 6681870 z^5 - 210336 z^6 + 2364 z^7 - 8 z^8) Sinh[2 Sqrt[z]] + 32 z^3 (9823275 - 29469825 z + 9823275 z^2 - 873180 z^3 + 26730 z^4 - 297 z^5 + z^6) SinhIntegral[2 Sqrt[z]])

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]