Portability | portable |
---|---|
Stability | experimental |
Maintainer | mik@konecny.aow.cz |
Internal module for Data.Number.ER.RnToRm.UnitDom.ChebyshevBase.Polynom.
Implementation of safely rounded integration of polynomials and other related functions.
- chplIntegrate :: (ERRealBase b, DomainBox box varid Int, Ord box) => varid -> ERChebPoly box b -> (ERChebPoly box b, ERChebPoly box b)
Documentation
:: (ERRealBase b, DomainBox box varid Int, Ord box) | |
=> varid | variable to integrate by |
-> ERChebPoly box b | |
-> (ERChebPoly box b, ERChebPoly box b) |
Approximate from below and from above the integral of a polynomial.
Based on the following formulas for Chebyshev polynomials:
\int T_n(x)dx = T_{n+1}(x)/2(n+1) - T_{n-1}(x)/2(n-1)
\int T_1(x)dx = T_2(x)/4 + 1/4
\int T_0(x)dx = T_1(x)