New Sum of Powers Log Function
04-01-2021, 11:05 PM
Post: #19
 Albert Chan Senior Member Posts: 1,793 Joined: Jul 2018
RE: New Sum of Powers Log Function
(04-01-2021 06:05 PM)Namir Wrote:  Does any of your previous analysis and approximations work on the following variants of the SopLog summations?

It depends on the function, and its argument. Eulerâ€“Maclaurin might not work.

Example, on your sdSum (I think you meant range(n,1,-1), or range(2,n+1) in reverse)
Code:
exact = lambda x,n,scale: 1 + fsum(k**(x*scale**(n-k)) for k in xrange(2,n+1)) guess = lambda x,n,scale: 1 + sumem(lambda k: k**(x*scale**(n-k)), [2,n])

>>> x, n, scale = 0.5, 100000, 0.5
>>> exact(x,n,scale), guess(x,n,scale)
(100337.09650943844, 100318.790872778)

Try a big x, guess is so wrong, it "sumed" negative !

>>> x = 1.5
>>> exact(x,n,scale), guess(x,n,scale)
(31728482.871558648, -38398120.2216635)
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 Messages In This Thread New Sum of Powers Log Function - Namir - 03-29-2021, 04:53 PM RE: New Sum of Powers Log Function - C.Ret - 03-29-2021, 08:39 PM RE: New Sum of Powers Log Function - Albert Chan - 03-29-2021, 10:47 PM RE: New Sum of Powers Log Function - Albert Chan - 03-30-2021, 01:44 AM RE: New Sum of Powers Log Function - Albert Chan - 03-30-2021, 08:35 PM RE: New Sum of Powers Log Function - Albert Chan - 03-30-2021, 10:26 PM RE: New Sum of Powers Log Function - Namir - 03-30-2021, 11:05 AM RE: New Sum of Powers Log Function - Albert Chan - 03-30-2021, 04:35 PM RE: New Sum of Powers Log Function - Paul Dale - 03-30-2021, 11:41 AM RE: New Sum of Powers Log Function - Gene - 03-30-2021, 01:43 PM RE: New Sum of Powers Log Function - C.Ret - 03-30-2021, 04:01 PM RE: New Sum of Powers Log Function - Namir - 03-30-2021, 05:56 PM RE: New Sum of Powers Log Function - Namir - 03-31-2021, 01:27 PM RE: New Sum of Powers Log Function - Albert Chan - 03-31-2021, 04:06 PM RE: New Sum of Powers Log Function - Albert Chan - 03-31-2021, 09:25 PM RE: New Sum of Powers Log Function - Namir - 03-31-2021, 02:19 PM RE: New Sum of Powers Log Function - Albert Chan - 04-01-2021, 02:56 PM RE: New Sum of Powers Log Function - Namir - 04-01-2021, 06:05 PM RE: New Sum of Powers Log Function - Albert Chan - 04-01-2021 11:05 PM RE: New Sum of Powers Log Function - Namir - 04-01-2021, 11:55 PM RE: New Sum of Powers Log Function - Albert Chan - 04-02-2021, 01:29 AM RE: New Sum of Powers Log Function - Albert Chan - 04-02-2021, 01:18 PM RE: New Sum of Powers Log Function - Namir - 04-04-2021, 03:41 PM

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