Explains why power series are inefficient for computing trig functions like cosine, using cos(200) as an example, and discusses range reduction.
Explores the function expq(x), its closed forms, differential equations, and relation to the Mittag-Leffler function.
Explores the Laplace limit and convergence of power series solutions to Kepler's equation, with Python code to compute the limit.
Explores the power series of exp(exp(y)) and the ratio of Bell numbers to factorials, relating partitions to permutations.
Explores a Gaussian approximation using cosine and sine functions, comparing it to the standard Gaussian density.
Explains why specialized sinpi() functions exist for accurate computation of trigonometric functions at half-integer multiples, avoiding floating-point errors.
