Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1667)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=9/2

http://functions.wolfram.com/07.22.03.1667.01

Input Form

HypergeometricPFQ[{-(5/2)}, {9/2, 11/2}, z] == (1/(2097152 z^(9/2))) (7 (2 Sqrt[z] (-141750 - 203175 z - 105840 z^2 - 54720 z^3 + 18492 z^4 - 836 z^5 + 8 z^6) Cosh[2 Sqrt[z]] + (141750 - 174825 z - 102060 z^2 - 40320 z^3 + 17700 z^4 - 828 z^5 + 8 z^6) Sinh[2 Sqrt[z]] - 8 z (-70875 - 85050 z - 47250 z^2 - 31500 z^3 + 9450 z^4 - 420 z^5 + 4 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]