Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aga4)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aga4.01

Input Form

HypergeometricPFQ[{21/4}, {9/2, -(19/4)}, z] == (1/(798145920 z^(7/2))) (-2 Sqrt[z] (-224847748125 - 168976489500 z - 45110520000 z^2 - 8370984960 z^3 - 1629388800 z^4 - 51118080 z^5 + 4194304 z^6) Cosh[2 Sqrt[z]] + 3 (-74949249375 - 156257829000 z - 63488880000 z^2 - 12831436800 z^3 - 2607022080 z^4 - 306708480 z^5 + 8388608 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]