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Frederick Williams
science forum addict

Joined: 19 Nov 2005
Posts: 97

Posted: Wed Jun 21, 2006 3:05 pm    Post subject: Re: Euler One

Jim Dars wrote:
 Quote: Hi All, I was just rereading William Dunham's "Euler - Master of Us All". Not as good as his wonderful "Journey Through Genius", but still a VERY interesting book. He points out Euler's solution(s) to find the value of Sum (1 to infinity on k) k^-i where i is an even integer (see Euler Two) and remarks that no one has yet found solutions for i being an odd integer greater than one. (Except for the 1978 "find" that for i=3 the answer is irrational.) Has any progress yet been made?

Yes, see http://mathworld.wolfram.com/RiemannZetaFunction.html.

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Jim Dars
science forum beginner

Joined: 03 Jul 2005
Posts: 41

Posted: Tue Jun 20, 2006 7:49 pm    Post subject: Euler One

Hi All,

I was just rereading William Dunham's "Euler - Master of Us All". Not as
good as his wonderful "Journey Through Genius", but still a VERY interesting
book.

He points out Euler's solution(s) to find the value of

Sum (1 to infinity on k) k^-i where i is an even integer (see Euler
Two)

and remarks that no one has yet found solutions for i being an odd integer
greater than one. (Except for the 1978 "find" that for i=3 the answer is
irrational.) Has any progress yet been made?

Best wishes, Jim
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 Topic Author Forum Replies Last Post Similar Topics Euler Two Jim Dars Recreational 0 Tue Jun 20, 2006 8:21 pm Euler Sum Generalized = Sum With Stirling Number Leroy Quet Math 1 Wed May 31, 2006 8:57 pm runge-kutta and euler methods RuiLopes4@gmail.com Math 2 Mon May 29, 2006 1:53 pm Euler totient larryhammick@telus.net Recreational 4 Sat May 20, 2006 3:59 am euler's phi-function and divisibility by primes Gottfried Helms Math 19 Mon May 08, 2006 6:51 pm

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