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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-1/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(1/2), -(21/4)}, z] == (1 + (88 z)/21 + (8320 z^2)/969 - (815104 z^3)/188955 + (131072 z^4)/264537 - (72876032 z^5)/416645775 - (8388608 z^6)/13749310575) Cosh[2 Sqrt[z]] - (1/13749310575) (2 Sqrt[z] (13749310575 + 63405342000 z + 3667023360 z^2 - 15583518720 z^3 + 3622502400 z^4 + 124780544 z^5) 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]