diff options
Diffstat (limited to 'buch/papers/laguerre/quadratur.tex')
| -rw-r--r-- | buch/papers/laguerre/quadratur.tex | 29 |
1 files changed, 29 insertions, 0 deletions
diff --git a/buch/papers/laguerre/quadratur.tex b/buch/papers/laguerre/quadratur.tex new file mode 100644 index 0000000..8ab1af5 --- /dev/null +++ b/buch/papers/laguerre/quadratur.tex @@ -0,0 +1,29 @@ +% +% quadratur.tex +% +% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule +% +\section{Gauss-Laguerre Quadratur +\label{laguerre:section:quadratur}} + +\begin{align} + \int_a^b f(x) w(x) + \approx + \sum_{i=1}^N f(x_i) A_i + \label{laguerre:gaussquadratur} +\end{align} + +\begin{align} + \int_{0}^{\infty} f(x) e^{-x} dx + \approx + \sum_{i=1}^{N} f(x_i) A_i + \label{laguerre:laguerrequadratur} +\end{align} + +\begin{align} + A_i + = + \frac{x_i}{(n + 1)^2 \left[ L_{n + 1}(x_i)\right]^2} + \label{laguerre:quadratur_gewichte} +\end{align} + |