Axel Vogt

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17 years, 185 days
Munich, Germany

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These are replies submitted by Axel Vogt

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

@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?

@Carl Love 

Oh ... that is worth to be posted as an extra thread.

Yes, multiply numerator and denominator by the conjugate here is the same as 'rationalize'.

Then the "complex division" vanishes and one proceedes as usual (guessing the x is some real), if one knows how to multiply complex numbers:

1/z = (1*conjugate(z)) / (z*conjugate(z)) = complex/real

1/(5*x-I): %= rationalize(%);

                            1       5 x + I
                         ------- = ---------
                         5 x - I       2
                                   25 x  + 1

 

Maple should stop that cancellations (except spam).

Please consider to introduce moving threads to some trash folder, but do not delete.

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