On Trigonometric Polynomials Satisfying Differential Equations

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Authors

  • H. L. Krall
     Department of Mathematics, Pennsylvania State University, University Park, (Penna) 16802 ,US
  • I. M. Sheffer
     Department of Mathematics, Pennsylvania State University, University Park, (Penna) 16802 ,US

Abstract

It is shown that the classical set {cos nx, sin nx} is the only real trigonometric polynomial set that satisfies a linear differential equation of the form Σ̅ ak (x)y(k)n(x) = λn yn (x) where λn is a parameter and the i coefficients {ak(x)} are independent of n.

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Published

1975-12-01

How to Cite

Krall, H. L., & Sheffer, I. M. (1975). On Trigonometric Polynomials Satisfying Differential Equations. The Journal of the Indian Mathematical Society, 39(1-4), 29–49. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16635

Issue

Volume 39, Issue 1-4, March-December 1975

Section

Articles

License

Copyright (c) 1975 H. L. Krall, I. M. Sheffer

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

G. SZECO: On Bi-Orthogonal Systems of Trigonometric Polynomials. Publications of the Mathematical Institute of the Hungarian Academy of Sciences, v. 8, Ser. A, Fasc. 3 (1963), 255-273.