- In mathematics,
Gegenbauer polynomials or
ultraspherical polynomials C(α) n(x) are
orthogonal polynomials on the
interval [−1,1] with
respect to the weight...
-
alternative to the
inverse DFT
definition is also available.[1]. The
Ultraspherical window was
introduced in 1984 by Roy
Streit and has
application in antenna...
- polynomials, also
called Rogers–Askey–Ismail
polynomials and
continuous q-
ultraspherical polynomials, are a
family of
orthogonal polynomials introduced by Rogers (1892...
- "sieved")
version of the
recurrence relations for
ultraspherical polynomials. For the
sieved ultraspherical polynomials of the
first kind the
recurrence relations...
- of an
orthogonal basis over the
angular coordinates is a
product of
ultraspherical polynomials, ∫ 0 π sin n − j − 1 ( φ j ) C s ( n − j − 1 2 ) cos ...
-
cannot be used). The
Chebyshev polynomials are a
special case of the
ultraspherical or
Gegenbauer polynomials C n ( λ ) ( x ) {\displaystyle C_{n}^{(\lambda...
-
Askey was at
Washington University,
Hirschman asked him to
solve an
ultraspherical polynomial problem.
Askey says in this lecture, "This led to a joint...
-
certain Lévy processes.
Sieved orthogonal polynomials, such as the
sieved ultraspherical polynomials,
sieved Jacobi polynomials, and
sieved Pollaczek polynomials...
- of the
Newton kernel (with
suitable normalization) are
precisely the
ultraspherical polynomials. Thus, the
zonal spherical harmonics can be
expressed as...
-
orthogonality measure for
several orthogonal polynomials. This
includes the q-
ultraspherical polynomials (also
known as the Askey–Ismail or Rogers–Askey–Ismail polynomials)...
