Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0471)

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=-3/2

http://functions.wolfram.com/07.22.03.0471.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(3/2), 11/2}, z] == (1/(17694720 z^(9/2))) (-2 Sqrt[z] (147349125 + 28066500 z - 1871100 z^2 - 1871100 z^3 - 653130 z^4 - 365760 z^5 - 948240 z^6 + 105624 z^7 - 2632 z^8 + 16 z^9) Cosh[2 Sqrt[z]] + (147349125 + 224532000 z - 16839900 z^2 + 5613300 z^3 + 2182950 z^4 + 880200 z^5 + 856080 z^6 - 103080 z^7 + 2616 z^8 - 16 z^9) Sinh[2 Sqrt[z]] + 32 z^7 (-124740 + 13365 z - 330 z^2 + 2 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]