Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1965)

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=-3/2, b_1`>=-11/2

For fixed z and a₁=-3/2, b₁=5/2

http://functions.wolfram.com/07.22.03.1965.01

Input Form

HypergeometricPFQ[{-(3/2)}, {5/2, 11/2}, z] == (1/(65536 z^(9/2))) (21 (-2 Sqrt[z] (945 - 180 z + 396 z^2 + 444 z^3 - 212 z^4 + 8 z^5) Cosh[2 Sqrt[z]] + (945 + 1080 z - 180 z^2 - 276 z^3 + 204 z^4 - 8 z^5) Sinh[2 Sqrt[z]] + 16 z^3 (90 + 135 z - 54 z^2 + 2 z^3) 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]