Let's get some information about this library package.
Library 'orthpoly': Calculation of orthogonal polynomials
Interface:
laguerre
gegenbauer
legendre
hermite
jacobi
chebyshev1
chebyshev2
The function chebyshev1 generates the nth Chebyshev polynomial of the first kind.
/ 3 \
poly \ - 3 x + 4 x , [x] /
The function chebyshev2 generates the nth Chebyshev polynomial of the second kind.
/ 2 4 \
poly \ - 12 x + 16 x + 1 , [x] /
The function gegenbauer generates the nth Gegenbauer polynomial.
/ 3 5 \
poly \ 24 x - 160 x + 192 x , [x] /
To generate the nth Hermite polynomial type:
/ 3 \
poly \ - 12 x + 8 x , [x] /
The function jacobi generates the nth Jacobi polynomial at a certain point.
/ 2 3 \
| 7 x 7 x 21 x |
poly | - --- - ---- + ----- + 1/2 , [x] |
\ 2 2 2 /
To generate the nth generalized Laguerre polynomial type:
/ 2 3 \
| 35 x 7 x x |
poly | - ---- + ---- - -- + 35/16 , [x] |
\ 8 4 6 /
And finally to generate the nth Legendre polynomial at a certain point type:
/ 2 4 \
| 15 x 35 x |
poly | - ----- + ----- + 3/8 , [x] |
\ 4 8 /