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

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 :-)

@mmcdara 

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 https://dlmf.nist.gov/10.51, 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.

Garch_estimation_using_Compile_Maple2021.mw

Here are the files, they got lost ...

_myGarch.mws
Garch.dll.zip
_myGarch.mws.pdf

And here a version using Compiler:-compile

Garch_estimation_using_Compile.mws

@Mariusz Iwaniuk : neat!

@acer sorry & thank you, I used 2017.3

MP_233942.mws

@Mariusz Iwaniuk you might give a reference

@vv : how you came up to involve the Catalan constant?