Bernstein bases and hahn—eberlein orthogonal polynomials

Abstract

Expansions of continuous and discrete Bernsein bases on shifted Jacobi and Hahn polynomials, respectively, are explicitly obtained in terms of Hahn-Eberlein orthogonal polynomials. The basic tool is an algorighm, recently developed by the authors, which allows one to solve the connection problem between two families of polynomials recurrently. ^∗

Keywords:

• orthogonal polynomilas, Bernstein bases,
• Bernstein bases,
• Hahn–Eberlein polynomials,
• Hahn polynomials,
• shifted Jacobi polynomials

MSC(1991):

• 33C25
• 68U07

^∗This work was partially supported by NATO grant CRG-960213. The work of I.A. and E. G. has been partially finantial supported by Xunta de Galicia-Universidade de Vigo under grant 64502I703. A.Z. also wish to acknowledge partial finaltial support from DGES (Ministerio de Educación y Cultura of Spain) under contract PG95-1205.

^∗This work was partially supported by NATO grant CRG-960213. The work of I.A. and E. G. has been partially finantial supported by Xunta de Galicia-Universidade de Vigo under grant 64502I703. A.Z. also wish to acknowledge partial finaltial support from DGES (Ministerio de Educación y Cultura of Spain) under contract PG95-1205.

Notes

^∗This work was partially supported by NATO grant CRG-960213. The work of I.A. and E. G. has been partially finantial supported by Xunta de Galicia-Universidade de Vigo under grant 64502I703. A.Z. also wish to acknowledge partial finaltial support from DGES (Ministerio de Educación y Cultura of Spain) under contract PG95-1205.

Additional information

Notes on contributors

A. Ronveaux

A. Zarzo

I. Area

E. Godoy