Results for: Special Functions

Three-Term Recurrence Relations and Bessel Functions

Three-term recurrence relations are the basis for computing Bessel functions. Contents A Familiar Three-Term Recurrence Friedrich Bessel Bessel Functions Miller's Algorithm ... read more >>

Ulps Plots Reveal Math Function Accuracy 2

"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more esoteric function like a Bessel function. The samples are compared with more accurate values obtained from a higher precision computation. A plot of the accuracy, measured in ulps, reveals valuable information about the underlying algorithms.... read more >>

Jahnke and Emde, Revisited 1

An incredible book, published in several editions from 1909 to 1933, by German mathematicians Eugene Jahnke and Fritz Emde, contains definitions and formulas for mathematical functions, hand-calculated tables of function values, and meticulous hand-drawn 2- and 3-dimensional graphs. An English edition was published by Dover in 1945.... read more >>

Iterated Powers Fractal 1

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Tower of Powers 1

I first investigated the tower of powers...

The Lambert W Function 1

The Lambert W function deserves to be better known. It pops up in all sorts of places. And our MATLAB function for evaluating the function is a beautiful use of the Halley method.... read more >>