Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0927)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=5/2

http://functions.wolfram.com/07.22.03.0927.01

Input Form

HypergeometricPFQ[{-(9/2)}, {5/2, 5/2}, z] == (1/(14745600 z^(3/2))) (2 Sqrt[z] (-416745 + 2245230 z - 729504 z^2 + 56064 z^3 - 1292 z^4 + 8 z^5) Cosh[2 Sqrt[z]] + (76545 + 1752030 z - 680040 z^2 + 54816 z^3 - 1284 z^4 + 8 z^5) Sinh[2 Sqrt[z]] - 8 (-42525 - 510300 z + 1275750 z^2 - 378000 z^3 + 28350 z^4 - 648 z^5 + 4 z^6) 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]