--- 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 6 2009, 10:43 pm

Newsgroups: sci.math

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

Date: Fri, 06 Nov 2009 23:43:08 +0100

Local: Fri, Nov 6 2009 10:43 pm

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

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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.

Studying the triangle of Eulerian numbers I came across the
idea to use this matrix for a summation, decomposing the entries
of the matrix into geometric series and derivatives.
Not much sophisticated reasoning about range of convergence
included, but it finds the correct value.

See:
http://go.helms-net.de/math/binomial_new/01_12_Eulermatrix.pdf

Chap. 2.2 and 2.3

How could this made waterproof?

TIA -

Gottfried Helms

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