Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adoq)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=11/4, b_1`>=-11/2

For fixed z and a₁=11/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.adoq.01

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), -(21/4)}, z] == (1/45589819275) ((45589819275 + 95521526100 z + 39502663200 z^2 + 7857622080 z^3 + 1092833280 z^4 + 158957568 z^5 + 154140672 z^6 + 4194304 z^7) Cosh[2 Sqrt[z]] + 6 Sqrt[z] (-15196606425 - 11578366800 z - 3132969840 z^2 - 500290560 z^3 - 66232320 z^4 - 12845056 z^5 + 9437184 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]