{"version":9,"randomSeed":"5933d562dc4ada13a44460074b52daa9","graph":{"viewport":{"xmin":-1.5994524262196856,"ymin":-3.10720531402836,"xmax":8.666793646950133,"ymax":4.134823127296413}},"expressions":{"list":[{"type":"folder","id":"49","title":"Taylor series"},{"type":"expression","id":"39","folderId":"49","color":"#c74440","latex":"\\frac{1}{1}\\left(x-1\\right)-\\frac{1}{2}\\left(x-1\\right)^{2}+\\frac{1}{3}\\left(x-1\\right)^{3}-\\frac{1}{4}\\left(x-1\\right)^{4}"},{"type":"expression","id":"41","folderId":"49","color":"#388c46","latex":"x-1-\\left(\\frac{1}{2}x^{2}-x+\\frac{1}{2}\\right)+\\left(\\frac{1}{3}x^{3}-x^{2}+x-\\frac{1}{3}\\right)-\\left(\\frac{1}{4}x^{4}-x^{3}+\\frac{3}{2}x^{2}-x+\\frac{1}{4}\\right)"},{"type":"expression","id":"50","folderId":"49","color":"#c74440","latex":"x-1-\\frac{1}{2}x^{2}+x-\\frac{1}{2}+\\frac{1}{3}x^{3}-x^{2}+x-\\frac{1}{3}-\\frac{1}{4}x^{4}+x^{3}-\\frac{3}{2}x^{2}+x-\\frac{1}{4}"},{"type":"expression","id":"53","folderId":"49","color":"#6042a6","latex":"-\\frac{25}{12}+4x-3x^{2}+\\frac{4}{3}x^{3}-\\frac{1}{4}x^{4}"},{"type":"folder","id":"55","title":"Padé approximant equations"},{"type":"expression","id":"25","folderId":"55","color":"#2d70b3","latex":"\\frac{A_{0}+A_{1}x+A_{2}x^{2}}{B_{0}+B_{1}x+B_{2}x^{2}}=-\\frac{25}{12}+4x-3x^{2}+\\frac{4}{3}x^{3}-\\frac{1}{4}x^{4}"},{"type":"expression","id":"62","folderId":"55","color":"#2d70b3","latex":"A_{0}+A_{1}x+A_{2}x^{2}=\\left(1+B_{1}x+B_{2}x^{2}\\right)\\left(-\\frac{25}{12}+4x-3x^{2}+\\frac{4}{3}x^{3}-\\frac{1}{4}x^{4}\\right)"},{"type":"expression","id":"63","folderId":"55","color":"#388c46","latex":"A_{0}+A_{1}x+A_{2}x^{2}=-\\frac{25}{12}+4x-3x^{2}+\\frac{4}{3}x^{3}-\\frac{1}{4}x^{4}-\\frac{25}{12}B_{1}x+4B_{1}x^{2}-3B_{1}x^{3}+\\frac{4}{3}B_{1}x^{4}-\\frac{1}{4}B_{1}x^{5}-\\frac{25}{12}B_{2}x^{2}+4B_{2}x^{3}-3B_{2}x^{4}+\\frac{4}{3}B_{2}x^{5}-\\frac{1}{4}B_{2}x^{6}"},{"type":"expression","id":"64","folderId":"55","color":"#6042a6","latex":"A_{0}+A_{1}x+A_{2}x^{2}=-\\frac{25}{12}+\\left(4-\\frac{25}{12}B_{1}\\right)x+\\left(-3+4B_{1}-\\frac{25}{12}B_{2}\\right)x^{2}+\\left(\\frac{4}{3}-3B_{1}+4B_{2}\\right)x^{3}+\\left(-\\frac{1}{4}+\\frac{4}{3}B_{1}-3B_{2}\\right)x^{4}+\\left(-\\frac{1}{4}B_{1}+\\frac{4}{3}B_{2}\\right)x^{5}+\\left(-\\frac{1}{4}B_{2}\\right)x^{6}"},{"type":"expression","id":"79","folderId":"55","color":"#388c46","latex":"A_{0}=-\\frac{25}{12}"},{"type":"expression","id":"80","folderId":"55","color":"#6042a6","latex":"A_{1}=4-\\frac{25}{12}B_{1}"},{"type":"expression","id":"81","folderId":"55","color":"#000000","latex":"A_{2}=-3+4B_{1}-\\frac{25}{12}B_{2}"},{"type":"expression","id":"83","folderId":"55","color":"#2d70b3","latex":"0=\\frac{4}{3}-3B_{1}+4B_{2}"},{"type":"expression","id":"84","folderId":"55","color":"#388c46","latex":"0=-\\frac{1}{4}+\\frac{4}{3}B_{1}-3B_{2}"},{"type":"expression","id":"85","folderId":"55","color":"#6042a6","latex":"B_{1}=\\frac{9}{11}"},{"type":"expression","id":"86","folderId":"55","color":"#000000","latex":"B_{2}=\\frac{37}{132}"},{"type":"expression","id":"87","folderId":"55","color":"#c74440"},{"type":"expression","id":"88","folderId":"55","color":"#2d70b3"},{"type":"text","id":"75","text":"final approximant function"},{"type":"expression","id":"76","color":"#000000","latex":"\\frac{A_{0}+A_{1}x+A_{2}x^{2}}{1+B_{1}x+B_{2}x^{2}}"},{"type":"expression","id":"40","color":"#2d70b3","latex":"\\ln x"}]}}