--- a hazardous summation-method for 0!-1!+2!-3!+...-... - sci.math

Message from discussion --- a hazardous summation-method for 0!-1!+2!-3!+...-...

Gottfried Helms

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More options Nov 7 2009, 7:09 am

Newsgroups: sci.math

From: Gottfried Helms <he...@uni-kassel.de>

Date: Sat, 07 Nov 2009 08:09:20 +0100

Local: Sat, Nov 7 2009 7:09 am

Subject: Re: --- a hazardous summation-method for 0!-1!+2!-3!+...-...

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Am 06.11.2009 23:43 schrieb Gottfried Helms:

> What do you think about the approach to the divergent summation of
> the series in the header

> su = 0! - 1! + 2! - 3! + 4! - ... + ...

> L Euler found a meaningful interpretation using integrals assigning
> it a value of about 0.596347…
> Also the Borel-summation assigns the same value to this.

I propose the following further values for variations of that sum:
fsum(x) = 0! + 1! x + 2! x^2 + 3! x^3 +…

fsum(-1) = 0.596347362323
fsum(-2) = 0.461455316242
fsum(-3) = 0.385602012137
fsum(-4) = 0.335221361210
fsum(-5) = 0.298669749329
fsum(-6) = 0.270633013639
fsum(-7) = 0.248281352547
fsum(-8) = 0.229947781627
fsum(-9) = 0.214577094581
fsum(-10) = 0.201464233646
fsum(-11) = 0.190117766778
fsum(-12) = 0.180183310425
… …

Could someone check this using the integral-formula?

Gottfried Helms

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