Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.5532)

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=-11/2

http://functions.wolfram.com/07.22.03.5532.01

Input Form

HypergeometricPFQ[{11/2}, {-(11/2), -(5/2)}, z] == (1 + (12 z)/5 + (224 z^2)/135 + (64 z^3)/63 + (512 z^4)/2025 - (2048 z^5)/6075 - (16384 z^6)/334125 - (16384 z^7)/147349125) Cosh[2 Sqrt[z]] - (1/147349125) (2 Sqrt[z] (147349125 + 157172400 z + 87318000 z^2 + 69189120 z^3 - 37255680 z^4 + 18063360 z^5 + 290816 z^6) Sinh[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]