Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0637)

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/07.22.03.0637.01

Input Form

HypergeometricPFQ[{-(11/2)}, {9/2, 9/2}, z] == (1/(97844723712 z^(7/2))) (-2 Sqrt[z] (6232166325 + 8735791680 z + 9710073450 z^2 - 9319272264 z^3 + 1292371290 z^4 - 58174992 z^5 + 1022892 z^6 - 7120 z^7 + 16 z^8) Cosh[2 Sqrt[z]] - (840591675 + 5273134020 z + 4832115750 z^2 - 8290220400 z^3 + 1239391206 z^4 - 57190248 z^5 + 1015860 z^6 - 7104 z^7 + 16 z^8) Sinh[2 Sqrt[z]] + 16 (442047375 + 1591370550 z + 2121827400 z^2 + 3300620400 z^3 - 2475465300 z^4 + 330062040 z^5 - 14669424 z^6 + 256608 z^7 - 1782 z^8 + 4 z^9) 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]