Power Series Articles

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6/7/2026 • EN

The Laplace limit

Explores the Laplace limit and convergence of power series solutions to Kepler's equation, with Python code to compute the limit.

Convergence Eccentricity Keplers Equation Laplace Limit Power Series

John D. Cook

6/4/2026 • EN

Partitions over permutations

Explores the power series of exp(exp(y)) and the ratio of Bell numbers to factorials, relating partitions to permutations.

Asymptotics Bell Numbers Partitions permutations Power Series

John D. Cook

5/31/2026 • EN

Another Gaussian approximation

Explores a Gaussian approximation using cosine and sine functions, comparing it to the standard Gaussian density.

Alternating Series Cosine Approximation Gaussian Approximation Power Series Truncation Error

John D. Cook

8/27/2014 • EN

O necessary sinpi

Explains why specialized sinpi() functions exist for accurate computation of trigonometric functions at half-integer multiples, avoiding floating-point errors.

Floating Point Accuracy Numerical Computing Power Series R Programming Trigonometric Functions

Thomas Lumley

Power Series Articles

The Laplace limit

Partitions over permutations

Another Gaussian approximation

O necessary sinpi

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