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

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.agkq.01

Input Form

HypergeometricPFQ[{23/4}, {1/2, -(21/4)}, z] == (1 + (80 z)/21 - (7680 z^2)/2261 + (8192 z^3)/62985 + (65536 z^4)/1322685 + (1048576 z^5)/138881925) Cosh[2 Sqrt[z]] + (1/13749310575) (4 Sqrt[z] (-13749310575 + 2756754000 z + 6296209920 z^2 - 1447649280 z^3 + 183828480 z^4 + 1048576 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]