Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0831)

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=-1/2

http://functions.wolfram.com/07.22.03.0831.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(1/2), 7/2}, z] == (1/(258048 z^(5/2))) (-2 Sqrt[z] (25515 - 22680 z - 33012 z^2 - 118512 z^3 + 31020 z^4 - 1504 z^5 + 16 z^6) Cosh[2 Sqrt[z]] + (25515 + 11340 z + 56700 z^2 + 94752 z^3 - 29604 z^4 + 1488 z^5 - 16 z^6) Sinh[2 Sqrt[z]] + 16 z^4 (-33075 + 7938 z - 378 z^2 + 4 z^3) 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]