catalan

Catalan constant

Syntax

catalan

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

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)

The Catalan constant is defined as follows:

$catalan = \sum_{i = 0}^{\infty} \frac{{(- 1)}^{i}}{{(2 i + 1)}^{2}} = \frac{1}{1^{2}} - \frac{1}{3^{2}} + \frac{1}{5^{2}} - \frac{1}{7^{2}} + \dots$

Introduced in R2014a