5.1. When x increases from the near right of 0 to 1, ln x increases as much as from near minus infinity to 1. This corresponds to the fact that when x increases as much as from near minus infinity to 0, ex increases only from the near above ...
SERENDIPITY IN MATHEMATICS OR HOW ONE IS LED TO DISCOVER THAT THE SUM FROM N=1 TO INFINITY OF THE PRODUCT OF ALL ODD NUMBERS LESS THAN 2-TIMES-N-MINUS-1 DIVIDED BY THE QUANTITY "N-TIMES-2-TO-THE-N-TIME-N-FACTORIAL EQUALS THE NATURAL LOGARITHM OF 4 ...
The natural log calculator (or simply ln calculator) determines the logarithm to the base of a famous mathematical constant, e, an irrational number with an approximate value of e = 2.71828. In other words, it calculates the natural logarithm. But, what is the natural logarithm, ln x, of ...
This is evident in the following equation, which specifies variational free energy (F) as the negative log probability of observations (õ) under a generative model (i.e., ‘surprise’) plus the Kullback–Leibler divergence (DKL) between the approximate posterior distribution and the true ...