Axel Vogt

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17 years, 218 days
Munich, Germany

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These are replies submitted by Axel Vogt

Done more carefully it is 3.60773264994268*10^29

Edit: uploaded according file

Have you estimated how many terms are involved?


Edit: moreover in one case you use LegendreP as summation index - that will not work. Try starting with "1" oder "2" instead of "9"

Here is a short way to get it in trigonometrics, like dharr, but using the parameters



f := 2*y^3*z - y^2 -2*m;
assume(m<0, 0<z); additionally(0 < discrim(f,y));




map(evalc@Im, S); # to show that all solutions are real

[0, 0, 0]


map(evalc@Re, S):
simplify(%, {discrim(f,y)=discr}): # more easy to read
Z:=simplify(%), discr = 'discrim(f,y)'; #%;

[(1/6)*(1+2*cos((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1)))/z, (1/6)*(-3^(1/2)*sin((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))-cos((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))+1)/z, (1/6)*(3^(1/2)*sin((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))-cos((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))+1)/z], discr = discrim(f, y)



Download MP_234277_CubicSolve_(2).mw

I am not aware that *all* the behaviour of Excel is really documented and thus would not expect that programs behave fine.

For the example '1: if you use the excel function length on it then it returns = 1, i.e. it is just a formatting convention (and more over: enter a date - it will have length 5).

So I suggest you convert to text in Excel (like a csv) and process in Maple.

PS: I almost never use that interface. On my german PC I always have to care for different decimal separators

Dividing by abs(y) you can reduce your question to "arctan(1,r)+arctan(-1,r) = 0 ?".

Or likewise to "argument(r+I)+argument(r-I) = 0 ?"

blindingly fast :-)


I used Maple 2017, and it runs beyond my patients if I used epsilon instead of absepsilon.

Searching the web a buzz word seems to be "contour polygon" which may help to define the area (not that I am used to arithmetic geometry)

@John2020 After I have been corrected by Carl Love I think you want j(n,z) in terms of sin and cos. For that you can use the recurrence relation, given in DLMF, and code it in a procedure.

... in Maple 2021 and Maple 2017

@Ali Guzel  You may take the sheet which uses Compiler:-compile.

The DLL is from 2004 and 20 years ago we had 32 bit, may be that Maple 2018 still had 32-Bit version - but concurrent Maple does not. Otherwise you would have to compile a new 64 bit DLL from the sources.

Here are the files, they got lost ...


And here a version using Compiler:-compile


@acer sorry & thank you, I used 2017.3


@Mariusz Iwaniuk you might give a reference

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