 About 1,950 results  books.google.com We prove a dual recurrence relation and a mixed ChristofFelDarbouxtype
formula, which expresses the derivative of an orthogonal polynomial in terms of
orthogonal polynomials and the modified associated polynomials. We exhibit ... 

 books.google.com Proof, (sketch) From the superstar conjugate (w.r.t. z) of the Christoffel Darboux
relation we find </>l(z)4>n((Xnl) ~ 4>n{z)<l>*n{anl) , , x y~, x — rj—, = 0„_i(^)k„
i Cfi(«nl)  Cn(Z) The superstar conjugate of this relation is K(z)K(anl) ... 

 books.google.com Christoffel—Darboux relation We shall now derive the Christoffel—Darboux
relation for the boundary situation. Theorem 11.3.1 (Christoffel—Darboux relation
). Let ¢n be the orthonormal functions in Ln and let H(z, w) and En be defined by
... 

 books.google.com 3 a dual recurrence relation by the way of an example how techniques which are
known for real orthogonal polynomials can be modified and used for the complex
case. But for deriving an analogue ChristoffelDarbouxtype formula which ... 

 books.google.com In our case the Christoffel Darboux relation takes the following form. THEOREM
5.3 (ChristoffelDarboux formula). Let{<j>k}k=0 wthfa € Ck\Cki be an orthonormal
basis for Cn, then the reproducing kernel kn(z, w) for Cn satisfies For this paper ... 

 books.google.com (4.6) This relation is called ChristoffelDarboux formula. It is important in the
theory of orthogonal polynomials. 4. Inverses of Toeplitz matrices. The proof of
the fact that inverses of Toeplitz matrices are TBezoutians follows the same lines
as ... 

 books.google.com Then c(xi Orthogonal polynomials are also known to satisfy the Christoffel
Darboux identity which is proved from the threeterms recurrence relationship. An
interesting open question was to know whether or not biorthogonal polynomials
or ... 

 books.google.com If n+lel then: i) *(K (z.y) (lzy)z) =  ii) *(K (z.y) (1zy)) =  0 (y) By using these
properties and the definition, it is easy to show that these kernels satisfy the
analogs of the Christoffel Darboux relation. Theorem 1. (First ChristoffelDarboux
relation) ... 

 books.google.com It indicates that it is much harder to extract information from the threeterm relation
(3.1) for d > 2. Among other consequences of the threeterm relation, we mention
an extension of the ChristoffelDarboux formula of one variable. Let Kn(., •) be ... 

 books.google.com known as the ChristoffelDarboux relation. Finally, one has the following property.
Property B.4 Let {pi}£0 denote the family of orthogonal polynomials with respect
to the weight function w. One can easily show that the infinite set ( j^ pk J^t0 is ... 

 