Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agd3)

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`=-11/2

http://functions.wolfram.com/07.22.03.agd3.01

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(9/4)}, -z] == (1 - (244 z)/99 + (928 z^2)/495 - (18496 z^3)/10395 + (4096 z^4)/4455 + (32768 z^5)/51975 - (1048576 z^6)/15436575 + (4194304 z^7)/30795967125) Cos[2 Sqrt[z]] + (1/2053064475) (2 Sqrt[z] (2053064475 - 2322658800 z + 1482077520 z^2 - 2224696320 z^3 - 755048448 z^4 - 383516672 z^5 + 5242880 z^6) Sin[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]