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| Keywords: Rational Elliptic Function (abs, n=4, x=(0,5)).svg rational elliptic function R<sub>4</sub> x over the interval 0 5 Here the selectivity factor is 1 4 Also shown is the discrimination factor L<sub>n</sub> own Inductiveload 2009-01-29 Mathematica Code <pre><nowiki> xp2xi_ Module g num den g Sqrt4 xi 2 + 4 xi 2 xi 2 - 1 2/3 ; num 2 xi 2 Sqrtg; den Sqrt8 xi 2 xi 2 + 1 + 12 g xi 2 - g 3 - Sqrtg 3; num/den ; xz2xi_ xi 2/xp2xi; txi_ Sqrt1 - 1/xi 2; Use the particular forms for these low-order REFs r1xi_ x_ x; r2xi_ x_ txi + 1 x 2 - 1 / txi - 1 x 2 + 1 ; r3xi_ x_ x 1 - xp2xi x 2 - xz2xi / 1 - xz2xi x 2 - xp2xi ; r4xi_ x_ Module num den num 1 + txi 1 + Sqrttxi 2 x 4 - 2 1 + txi 1 + Sqrttxi x 2 + 1; den 1 + txi 1 - Sqrttxi 2 x 4 - 2 1 + txi 1 - Sqrttxi x 2 + 1; num/den ; LogPlot xi 1 4; Absr4xi x x 0 5 PlotRange -> 0 01 100000 </nowiki></pre> Rational functions XY plots Special functions | ||||
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