# Cleve’s Corner: Cleve Moler on Mathematics and ComputingScientific computing, math & more

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# Three-Term Recurrence Relations and Bessel Functions

Posted by Cleve Moler,

Three-term recurrence relations are the basis for computing Bessel functions.... read more >>

# Ulps Plots Reveal Math Function Accuracy2

Posted by Cleve Moler,

"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, Revisited1

Posted by Cleve Moler,

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 >>