August 29th, 2012, 10:01 PM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Computation of L(4)
Define I am able to calculate it only for z = 2,3. Mathematica overflows if I try to calculate L(4). Any idea how to compute L(4) ? Any help will be appreciated, Balarka . 
August 30th, 2012, 08:00 AM  #2 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Computation of L(4)
What does the subscript of n mean? Pochhammer symbol?

August 30th, 2012, 08:12 AM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Computation of L(4) Quote:
 
August 30th, 2012, 09:15 AM  #4 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Computation of L(4)
Ah, OK. That's easier to write than the double up arrow notation. I doubt you'll be able to. The number has about digits. You'd need nearly 3 terabytes of memory just to store that number. Supercomputers can do it, but ours can't. Therefore I must stop calculating after two terms. with a LOT of zeroes following. I'd say that it's practically equal to 65537/65536. With this you could make almost integers. 
August 30th, 2012, 10:28 PM  #5 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Computation of L(4)
Ok, another question related to L(z) : Mathematica says diverges. How can we prove this? Thanks in advance, Balarka . 
August 31st, 2012, 05:02 AM  #6 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Computation of L(4)
I don't see why it would say that. It converges substantially faster than the series for e. Clearly from the definition in your original post. The second term goes to zero, and the subsequent terms are smaller and go to zero quicker. The First term is always one.

August 31st, 2012, 05:23 AM  #7  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Computation of L(4) Quote:
 
August 31st, 2012, 05:25 AM  #8 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Computation of L(4) . The limit of the remaining terms goes go zero faster. This is because .

August 31st, 2012, 05:35 AM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Computation of L(4) Quote:
2 > e^(1/e) Balarka .  
August 31st, 2012, 05:40 AM  #10  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Computation of L(4) Quote:
 

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