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LambertWeCoe.cin - Revision history
2024-03-29T02:00:53Z
Revision history for this page on the wiki
MediaWiki 1.31.16
https://mizugadro.mydns.jp/t/index.php?title=LambertWeCoe.cin&diff=28453&oldid=prev
T: Text replacement - "\$([^\$]+)\$" to "\\(\1\\)"
2019-07-30T09:48:28Z
<p>Text replacement - "\$([^\$]+)\$" to "\\(\1\\)"</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 09:48, 30 July 2019</td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>// [[LambertWeCoe.cin]] is the part of the [[C++]] code that evaluates the [[LambertW]] function in vicinity of <del class="diffchange diffchange-inline">$</del>-1/\mathrm e<del class="diffchange diffchange-inline">$</del>.</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>// [[LambertWeCoe.cin]] is the part of the [[C++]] code that evaluates the [[LambertW]] function in vicinity of <ins class="diffchange diffchange-inline">\(</ins>-1/\mathrm e<ins class="diffchange diffchange-inline">\)</ins>.</div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>// The declaration below defines the array of coefficients <del class="diffchange diffchange-inline">$</del>c<del class="diffchange diffchange-inline">$</del> in the expansion </div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>// The declaration below defines the array of coefficients <ins class="diffchange diffchange-inline">\(</ins>c<ins class="diffchange diffchange-inline">\)</ins> in the expansion </div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> // <del class="diffchange diffchange-inline">$</del>\displaystyle \mathrm{LambertW}\Big(\frac{-1}{\mathrm e} + \frac{t^2}{2\mathrm e}\Big)= <del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle \sum_{n=0}^{\infty}\, c_n t_n=<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>-1 +t<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle -\frac{t^2}{3}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle +\frac{11 t^3}{72}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle -\frac{43 t^4}{540}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle +\frac{769 t^5}{17280}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle - \frac{221 t^6}{8505}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle +\frac{680863 t^7}{43545600}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle -\frac{1963 t^8}{204120}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle +\frac{226287557 t^9}{37623398400}<del class="diffchange diffchange-inline">$</del> <del class="diffchange diffchange-inline">$</del>\displaystyle -\frac{5776369 t^{10}}{1515591000} +..<del class="diffchange diffchange-inline">$</del></div></td>
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<td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> // <ins class="diffchange diffchange-inline">\(</ins>\displaystyle \mathrm{LambertW}\Big(\frac{-1}{\mathrm e} + \frac{t^2}{2\mathrm e}\Big)= <ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle \sum_{n=0}^{\infty}\, c_n t_n=<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>-1 +t<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle -\frac{t^2}{3}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle +\frac{11 t^3}{72}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle -\frac{43 t^4}{540}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle +\frac{769 t^5}{17280}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle - \frac{221 t^6}{8505}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle +\frac{680863 t^7}{43545600}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle -\frac{1963 t^8}{204120}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle +\frac{226287557 t^9}{37623398400}<ins class="diffchange diffchange-inline">\)</ins> <ins class="diffchange diffchange-inline">\(</ins>\displaystyle -\frac{5776369 t^{10}}{1515591000} +..<ins class="diffchange diffchange-inline">\)</ins></div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>double LambertWeCoe[102]={ -1., 1.,</div></td>
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<td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>double LambertWeCoe[102]={ -1., 1.,</div></td>
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https://mizugadro.mydns.jp/t/index.php?title=LambertWeCoe.cin&diff=937&oldid=prev
Maintenance script at 06:01, 20 June 2013
2013-06-20T06:01:38Z
<p></p>
<p><b>New page</b></p><div>// [[LambertWeCoe.cin]] is the part of the [[C++]] code that evaluates the [[LambertW]] function in vicinity of $-1/\mathrm e$.<br />
// The declaration below defines the array of coefficients $c$ in the expansion <br />
<br />
// $\displaystyle \mathrm{LambertW}\Big(\frac{-1}{\mathrm e} + \frac{t^2}{2\mathrm e}\Big)= $ $\displaystyle \sum_{n=0}^{\infty}\, c_n t_n=$ $-1 +t$ $\displaystyle -\frac{t^2}{3}$ $\displaystyle +\frac{11 t^3}{72}$ $\displaystyle -\frac{43 t^4}{540}$ $\displaystyle +\frac{769 t^5}{17280}$ $\displaystyle - \frac{221 t^6}{8505}$ $\displaystyle +\frac{680863 t^7}{43545600}$ $\displaystyle -\frac{1963 t^8}{204120}$ $\displaystyle +\frac{226287557 t^9}{37623398400}$ $\displaystyle -\frac{5776369 t^{10}}{1515591000} +..$<br />
<br />
double LambertWeCoe[102]={ -1., 1.,<br />
-0.3333333333333333333,<br />
0.1527777777777777778,<br />
-0.0796296296296296296,<br />
0.0445023148148148148,<br />
-0.0259847148736037625,<br />
0.0156356325323339212,<br />
-0.00961689202429943171,<br />
0.00601454325295611786,<br />
-0.00381129803489199923,<br />
0.00244087799114398267,<br />
-0.00157693034468678425,<br />
0.00102626332050760715,<br />
-0.000672061631156136204,<br />
0.00044247306181462091,<br />
-0.000292677224729627445,<br />
0.000194387276054539318,<br />
-0.000129574266852748819,<br />
0.0000866503580520812717,<br />
-0.0000581136075044138168,<br />
0.0000390766848674390516,<br />
-0.0000263380647472310987,<br />
0.0000177903458050795854,<br />
-0.0000120403527395599769,<br />
8.16353198249661217e-6,<br />
-5.54420320856735914e-6,<br />
3.77109496110725341e-6,<br />
-2.56870503905509544e-6,<br />
1.7520067268263412e-6,<br />
-1.19644530891572567e-6,<br />
8.17994056528003472e-7,<br />
-5.59855188137879574e-7,<br />
3.83566385149181379e-7,<br />
-2.63037861927186308e-7,<br />
1.80544727751016444e-7,<br />
-1.24027544004224703e-7,<br />
8.52703516168582825e-8,<br />
-5.86686308977225918e-8,<br />
4.03947301280155627e-8,<br />
-2.78316209626026845e-8,<br />
1.91881310685738554e-8,<br />
-1.32371244669424267e-8,<br />
9.13710905680806547e-9,<br />
-6.3105381623506781e-9,<br />
4.3606925472094428e-9,<br />
-3.01485057758130614e-9,<br />
2.08539250292067727e-9,<br />
-1.44315359778020971e-9,<br />
9.9915217179721807e-10,<br />
-6.92049499350375257e-10,<br />
4.79536537580206161e-10,<br />
-3.32413217764048006e-10,<br />
2.30515597891712908e-10,<br />
-1.59912196300685515e-10,<br />
1.10972718669265744e-10,<br />
-7.70368786717788538e-11,<br />
5.34962929680470565e-11,<br />
-3.71609045080338343e-11,<br />
2.58215148167552937e-11,<br />
-1.79475645333454047e-11,<br />
1.24782428944225017e-11,<br />
-8.67803499992131116e-12,<br />
6.03678282054492658e-12,<br />
-4.20051193774766886e-12,<br />
2.92353237458081712e-12,<br />
-2.03525702096338716e-12,<br />
1.41720636451186404e-12,<br />
-9.87066370244645293e-13,<br />
6.87632082200663056e-13,<br />
-4.79136913828980365e-13,<br />
3.33929038076548621e-13,<br />
-2.327754844257851e-13,<br />
1.62295447584966799e-13,<br />
-1.13177248655861478e-13,<br />
7.89393171526768803e-14,<br />
-5.50689596325770156e-14,<br />
3.84235573773504502e-14,<br />
-2.68141146603903671e-14,<br />
1.87155512160818899e-14,<br />
-1.30651139440572381e-14,<br />
9.12207036595587938e-15,<br />
-6.37003114897626912e-15,<br />
4.44893399727651941e-15,<br />
-3.10767106994306571e-15,<br />
2.17108719363861928e-15,<br />
-1.51698449707275936e-15,<br />
1.06009611885002865e-15,<br />
-7.40914663180577404e-16,<br />
5.17903258763594061e-16,<br />
-3.62063975903811412e-16,<br />
2.53149433731430854e-16,<br />
-1.77020013639351241e-16,<br />
1.23799924052967824e-16,<br />
-8.65904219941911638e-17,<br />
6.05716926896423085e-17,<br />
-4.23758948025618507e-17,<br />
2.96494297432517426e-17,<br />
-2.07472769988816835e-17,<br />
1.45195179941344395e-17,<br />
-1.01622223292926686e-17,<br />
7.1132762840052161e-18};<br />
<br />
// [[Category:LambertW]]<br />
// [[Category:C++]]<br />
// [[Category:Mathematica]]</div>
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