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April 18th, 2012, 11:20 PM   #1
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eulers constant

Is it possible to prove that eulers constant is transcendental?
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April 18th, 2012, 11:31 PM   #2
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Re: eulers constant

Yes.

Do a search on "proof that e is transcendental" in your favorite search engine and you will find many proofs.
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April 18th, 2012, 11:42 PM   #3
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Re: eulers constant

No,not nepiers constant, i mean euler mascheroni constant
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April 18th, 2012, 11:49 PM   #4
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Re: eulers constant

Ah, I wondered about whether you meant Napier's constant, which I've seen also referred to as Euler's constant. From Wikipedia:

Quote:
The number ? has not been proved algebraic or transcendental. In fact, it is not even known whether ? is irrational. Continued fraction analysis reveals that if ? is rational, its denominator must be greater than
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April 19th, 2012, 12:06 AM   #5
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Re: eulers constant

Thanx.

Can you show me how the limit of the difference of the harmonic series and natural logarithm output such a number????? I think your explanation will be much easier than other text books.
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April 19th, 2012, 12:18 AM   #6
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Re: eulers constant

That is simply how it is defined, from my limited understanding of it.

I'm sure someone who actually knows something about this constant will weigh in.
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April 19th, 2012, 12:30 AM   #7
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Re: eulers constant

Quote:
I'm sure someone who actually knows something about this constant will weigh in.
I hope so.
Thank you for all that informations, its useful to me
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April 19th, 2012, 05:18 AM   #8
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Re: eulers constant

Quote:
Originally Posted by MarkFL
That is simply how it is defined, from my limited understanding of it.
Yes, that's the usual definition.

I should mention that I think of as the logarithm of a more fundamental constant, Somehow it's natural that the limit, involving logarithms as it does, has a constant which is the logarithm of the fundamental one.

I should mention at this point that is also believed to be transcendental but not even known to be rational. If it is rational the denominator is large.
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April 19th, 2012, 07:52 AM   #9
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Re: eulers constant

But is it possible to derive euler mascheroni constant from that formula
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April 19th, 2012, 01:21 PM   #10
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Re: eulers constant

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Originally Posted by mathbalarka
But is it possible to derive euler mascheroni constant from that formula
Yes, though it converges slowly.
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