New Sum of Powers Log Function
04-01-2021, 11:55 PM (This post was last modified: 04-02-2021 01:24 AM by Namir.)
Post: #20
 Namir Senior Member Posts: 813 Joined: Dec 2013
RE: New Sum of Powers Log Function
(04-01-2021 11:05 PM)Albert Chan Wrote:
(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. Euler–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)

I am looking to solve for x given all other parameters--n, s, scale and leading to a zero value for s - sum_of_series.
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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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