Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0443)

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=-5/2

http://functions.wolfram.com/07.22.03.0443.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(5/2), 11/2}, z] == (1/(14745600 z^(9/2))) (2 Sqrt[z] (-343814625 - 88877250 z + 5613300 z^2 + 1247400 z^3 + 180450 z^4 + 36180 z^5 + 15360 z^6 + 34784 z^7 - 1752 z^8 + 16 z^9) Cosh[2 Sqrt[z]] + (343814625 + 547296750 z - 9355500 z^2 + 6237000 z^3 + 935550 z^4 + 151380 z^5 + 41520 z^6 + 33120 z^7 - 1736 z^8 + 16 z^9) Sinh[2 Sqrt[z]] - 32 z^8 (4455 - 220 z + 2 z^2) 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]