# Plotting number of accurate digits as function of n

## Mathematica program

 ```(* Plotting number of accurate digits as function of n *) sect = "errors"; entity = "figure"; shape[0] := MakeSymbol[Disk[{0, 0}, Offset[5 scale{1, 1}]]];(*partial sums*) shape[1] := MakeSymbol[ Circle[{0, 0}, Offset[6 scale{1, 1}]]];(*linear (Pade) approximants*) shape[2] := PlotSymbol[Box, 5 scale];(*quadratic*) shape[3] := PlotSymbol[Triangle, 6 scale];(*cubic*) shape[4] := PlotSymbol[Diamond, 6 scale];(*quartic*) shape[5] := PlotSymbol[Star, 6 scale];(*5th order*) shape[6] := MakeSymbol[{RegularPolygon[6, 6 scale, {0, 0}, 0, 2], RegularPolygon[6, 6 scale, {0, 0}, Pi/3, 2]}];(*6th order*) color[n_] := RGBColor[0, 0, 0]; color[0] := RGBColor[1, 0, 0]; color[1] := RGBColor[0, 0, 1]; color[2] := RGBColor[0, 1, 0]; If[newfigure == True, degrs = {0, 1, 2, 3, 4, 5, 6}; Get["erralgap.txt", Path -> {"C:\\sergeev\\umassd\\math\\series"}]; scale = 0.5 30./(15 + nm); mdegrs = Length[degrs]; plts = {}; Do[degr = degrs[[ndegr]]; errlist = If[degr === 0, Table[err = Abs[enex - Plus @@ Take[func, n]]; logerr = -Log[10, err]; {n, logerr}, {n, nm}], erralgappr[name, degr]]; If[Length[errlist] > 2 && ! List @@ errlist == {name, degr}, plt = MultipleListPlot[errlist, SymbolShape -> shape[degr], SymbolStyle -> {{AbsoluteThickness[1.2 scale], color[degr]}}, PlotStyle -> {{AbsoluteThickness[1.2 scale], RGBColor[1, 0, 0]}}, PlotJoined -> (degr === 0), DisplayFunction -> Identity]; plts = Append[plts, plt]], {ndegr, mdegrs}]; plt = Show[plts, plt0, Frame -> True, FrameLabel -> {"\!\(\* StyleBox[\"n\",\nFontFamily->\"Times\",\nFontSlant->\"Italic\"]\)", "\!\(\* StyleBox[\"number\ \ \ \ of\ \ \ accurate\ \ \ digits\",\nFontFamily->\"Times\",\nFontSize->9]\)"}, AspectRatio -> rat, PlotRange -> {{0, nm + 0.3}, All}, AxesOrigin -> {0, 0}, DisplayFunction -> Identity]; outfile = ToFileName[dir, sect <> ".gif"]; Export[outfile, plt, "GIF", ImageSize -> 320 {1, rat}, ImageResolution -> 150]; outfile1 = StringReplace[outfile, ".gif" -> ".pdf"]; plt1 = Show[plt, PlotRegion -> {{0.05, 0.95}, {0.05, 0.95}}, DisplayFunction -> Identity]; Export[outfile1, plt1, "PDF", ImageSize -> Automatic, ImageOffset -> Automatic, ImageRotated -> True]; ]; " sect <> "\">
" // p; "" // p; "" // p; "" <> "
Convergence of summation approximants for the Moller - Plesset series
measured in growth of number of accurate decimal digits of summation results
with increase of n, number of used coefficients.
The summation methods are partial sums (red connected disks),