catalan

Catalan constant

Syntax

catalan

Description

catalan represents the Catalan constant. To get a floating-point approximation with the current precision set by digits, use vpa(catalan).

Examples

Approximate Catalan Constant

Find a floating-point approximation of the Catalan constant with the default number of digits and with the 10-digit precision.

Use vpa to approximate the Catalan constant with the default 32-digit precision:

vpa(catalan)

ans =
0.91596559417721901505460351493238

Set the number of digits to 10 and approximate the Catalan constant:

old = digits(10);
vpa(catalan)

ans =
0.9159655942

Restore the default number of digits:

digits(old)

More About

Catalan Constant

The Catalan constant is defined as follows:

$$\mathrm{catalan}={\displaystyle \sum _{i=0}^{\infty }\frac{{\left(-1\right)}^i}{{\left(2i+1\right)}^2}}=\frac{1}{1^2}-\frac{1}{3^2}+\frac{1}{5^2}-\frac{1}{7^2}+\dots$$

Version History

Introduced in R2014a