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

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`=-7/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(7/2), -(17/4)}, -z] == (1/68746552875) ((68746552875 - 164067403500 z + 110018185200 z^2 - 54353376000 z^3 + 56628633600 z^4 + 195052830720 z^5 - 9903800320 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] + 10 Sqrt[z] (13749310575 - 14481066600 z + 7584192000 z^2 - 4044902400 z^3 + 17429102592 z^4 - 6635913216 z^5 + 67108864 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]