Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.4562)

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=4, b_1`>=-11/2

For fixed z and a₁=4, b₁=-11/2

http://functions.wolfram.com/07.22.03.4562.01

Input Form

HypergeometricPFQ[{4}, {-(11/2), 6}, z] == (1/(4158 z^5)) ((82495863450 + 163027539675 z + 51068867850 z^2 + 6023507490 z^3 + 349188840 z^4 + 10812384 z^5 + 158976 z^6 + 512 z^7) Cosh[2 Sqrt[z]] - 3 (-654729075 (-42 + z) + 2 Sqrt[z] (27498621150 + 17677685025 z + 3229996770 z^2 + 261891630 z^3 + 11085360 z^4 + 244928 z^5 + 2048 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]