April 18th, 2012, 11:20 PM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  eulers constant
Is it possible to prove that eulers constant is transcendental?

April 18th, 2012, 11:31 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  Re: eulers constant
Yes. Do a search on "proof that e is transcendental" in your favorite search engine and you will find many proofs. 
April 18th, 2012, 11:42 PM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: eulers constant
No,not nepiers constant, i mean euler mascheroni constant

April 18th, 2012, 11:49 PM  #4  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  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:
 
April 19th, 2012, 12:06 AM  #5 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  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. 
April 19th, 2012, 12:18 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  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. 
April 19th, 2012, 12:30 AM  #7  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: eulers constant Quote:
Thank you for all that informations, its useful to me  
April 19th, 2012, 05:18 AM  #8  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: eulers constant Quote:
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.  
April 19th, 2012, 07:52 AM  #9 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: eulers constant
But is it possible to derive euler mascheroni constant from that formula

April 19th, 2012, 01:21 PM  #10  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: eulers constant Quote:
 

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