.. _func-Chebyshev:

=========
Chebyshev
=========

.. index:: Chebyshev

Description
-----------

This function calculates a partial Chebyshev expansion

.. math:: \sum_{n=0}^N a_n T_n(a+bx)

where :math:`a_n` are the expansion coefficients and :math:`T_n(x)` are
Chebyshev polynomials of the first kind defined by the reccurence
relation

.. math:: T_0(x)=1 \,\!

.. math:: T_1(x)=x \,\!

.. math:: T_{n+1}(x)= 2xT_n(x)-T_{n-1}(x) \,\!

Coefficients :math:`a` and :math:`b` are defined to map the fitting
interval into [-1,1] interval.

Chebyshev function has tree attributes (non-fitting parameters). First
is 'n' which has integer type and sets the expansion order and creates
n+1 expansion coefficients (fitting parameters). The parameter names
have the form 'Ai' where 'A' is letter 'A' and 'i' is the parameter's
index starting from 0.

The other two attributes are doubles 'StartX' and 'EndX' which define
the expansion (fitting) interval.

.. attributes::

.. properties::

.. categories::

.. sourcelink::