# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.analysis.integration.univariate.riemann.substitution

## Class MixedRule

• All Implemented Interfaces:
SubstitutionRule

public class MixedRule
extends DoubleExponential
The mixed rule is good for functions that fall off rapidly at infinity, e.g., $$e^{x^2}$$ or $$e^x$$ The integral region is $$(0, +\infty)$$. The tricky part of using this transformation is to figure out a good range for t. If there is information about the integrand available, SubstitutionRule.ta() and SubstitutionRule.tb() should be overridden. The substitution is $x = e^{t - e^{-t}}$
• ### Constructor Detail

• #### MixedRule

public MixedRule(UnivariateRealFunction f,
double a,
double b,
double c)
Construct a MixedRule substitution rule.
Parameters:
f - the integrand
a - the lower limit
b - the upper limit
c - usually either 0 or 0.5 * PI