New Sum of Powers Log Function

[Namir]

Hi All,

I just published a new function on my web site. The function is SopLog which is short for “Sum of Powers Logarithm”. The function is defined as SolLogN(S) = x where N is an integer base (number of integers to add), S is the sum of terms, and x is the power to which is integer is raised. This means that:

S = sum i^x for i=1 to N

The power x is calculated as the root of the following function:

S – sum i^x for i=1 to N

You can download the article here. The article contains listings for SopLog in Excel VBA, Matlab, Python, C++, HP-71B BASIC, Generic legacy Pocket Computer BASIC, HP-41C, HP-41CX (with and without the Advantage module), HP-67/97, and HP-15C.

The article also shows an empirical relationship between x, S, and N.

The SopLog function is good for bench-marking. I leave it to other math-oriented folks to find other uses for SopLog.

Enjoy!

Namir