Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0381)

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=-9/2

http://functions.wolfram.com/07.22.03.0381.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(9/2), 11/2}, z] == (1/(58060800 z^(9/2))) (2 Sqrt[z] (-6188663250 - 2161120500 z + 42567525 z^2 + 935550 z^3 + 28350 z^4 + 1260 z^5 + 90 z^6 + 12 z^7 + 4 z^8 + 8 z^9) Cosh[2 Sqrt[z]] + (6188663250 + 10412671500 z + 638512875 z^2 + 12162150 z^3 + 311850 z^4 + 11340 z^5 + 630 z^6 + 60 z^7 + 12 z^8 + 8 z^9) Sinh[2 Sqrt[z]] - 32 z^10 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]