LambertWeCoe.cin

// LambertWeCoe.cin is the part of the C++ code that evaluates the LambertW function in vicinity of \(-1/\mathrm e\). // The declaration below defines the array of coefficients \(c\) in the expansion

// \(\displaystyle \mathrm{LambertW}\Big(\frac{-1}{\mathrm e} + \frac{t^2}{2\mathrm e}\Big)= \) \(\displaystyle \sum_{n=0}^{\infty}\, c_n t_n=\) \(-1 +t\) \(\displaystyle -\frac{t^2}{3}\) \(\displaystyle +\frac{11 t^3}{72}\) \(\displaystyle -\frac{43 t^4}{540}\) \(\displaystyle +\frac{769 t^5}{17280}\) \(\displaystyle - \frac{221 t^6}{8505}\) \(\displaystyle  +\frac{680863 t^7}{43545600}\) \(\displaystyle -\frac{1963 t^8}{204120}\) \(\displaystyle +\frac{226287557 t^9}{37623398400}\) \(\displaystyle -\frac{5776369 t^{10}}{1515591000} +..\)

double LambertWeCoe[102]={ -1., 1., -0.3333333333333333333, 0.1527777777777777778, -0.0796296296296296296, 0.0445023148148148148, -0.0259847148736037625, 0.0156356325323339212, -0.00961689202429943171, 0.00601454325295611786, -0.00381129803489199923, 0.00244087799114398267, -0.00157693034468678425, 0.00102626332050760715, -0.000672061631156136204, 0.00044247306181462091, -0.000292677224729627445, 0.000194387276054539318, -0.000129574266852748819, 0.0000866503580520812717, -0.0000581136075044138168, 0.0000390766848674390516, -0.0000263380647472310987, 0.0000177903458050795854, -0.0000120403527395599769, 8.16353198249661217e-6, -5.54420320856735914e-6, 3.77109496110725341e-6, -2.56870503905509544e-6, 1.7520067268263412e-6, -1.19644530891572567e-6, 8.17994056528003472e-7, -5.59855188137879574e-7, 3.83566385149181379e-7, -2.63037861927186308e-7, 1.80544727751016444e-7, -1.24027544004224703e-7, 8.52703516168582825e-8, -5.86686308977225918e-8, 4.03947301280155627e-8, -2.78316209626026845e-8, 1.91881310685738554e-8, -1.32371244669424267e-8, 9.13710905680806547e-9, -6.3105381623506781e-9, 4.3606925472094428e-9, -3.01485057758130614e-9, 2.08539250292067727e-9, -1.44315359778020971e-9, 9.9915217179721807e-10, -6.92049499350375257e-10, 4.79536537580206161e-10, -3.32413217764048006e-10, 2.30515597891712908e-10, -1.59912196300685515e-10, 1.10972718669265744e-10, -7.70368786717788538e-11, 5.34962929680470565e-11, -3.71609045080338343e-11, 2.58215148167552937e-11, -1.79475645333454047e-11, 1.24782428944225017e-11, -8.67803499992131116e-12, 6.03678282054492658e-12, -4.20051193774766886e-12, 2.92353237458081712e-12, -2.03525702096338716e-12, 1.41720636451186404e-12, -9.87066370244645293e-13, 6.87632082200663056e-13, -4.79136913828980365e-13, 3.33929038076548621e-13, -2.327754844257851e-13, 1.62295447584966799e-13, -1.13177248655861478e-13, 7.89393171526768803e-14, -5.50689596325770156e-14, 3.84235573773504502e-14, -2.68141146603903671e-14, 1.87155512160818899e-14, -1.30651139440572381e-14, 9.12207036595587938e-15, -6.37003114897626912e-15, 4.44893399727651941e-15, -3.10767106994306571e-15, 2.17108719363861928e-15, -1.51698449707275936e-15, 1.06009611885002865e-15, -7.40914663180577404e-16, 5.17903258763594061e-16, -3.62063975903811412e-16, 2.53149433731430854e-16, -1.77020013639351241e-16, 1.23799924052967824e-16, -8.65904219941911638e-17, 6.05716926896423085e-17, -4.23758948025618507e-17, 2.96494297432517426e-17, -2.07472769988816835e-17, 1.45195179941344395e-17, -1.01622223292926686e-17, 7.1132762840052161e-18};

// // //