Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0497)

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=-1/2

http://functions.wolfram.com/07.22.03.0497.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 11/2}, z] == (1/(23592960 z^(9/2))) (2 Sqrt[z] (-49116375 - 4677750 z - 467775 z^2 + 2182950 z^3 + 2326140 z^4 + 7875720 z^5 - 1944930 z^6 + 106052 z^7 - 1756 z^8 + 8 z^9) Cosh[2 Sqrt[z]] + (49116375 + 70166250 z - 10758825 z^2 + 3430350 z^3 + 4365900 z^4 + 6412680 z^5 - 1848030 z^6 + 104340 z^7 - 1748 z^8 + 8 z^9) Sinh[2 Sqrt[z]] - 32 z^6 (1091475 - 249480 z + 13365 z^2 - 220 z^3 + z^4) 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]