The Journal of the Indian Mathematical Society

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On Trigonometric Polynomials Satisfying Differential Equations


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1 Department of Mathematics, Pennsylvania State University, University Park, (Penna) 16802, United States
     

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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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  • On Trigonometric Polynomials Satisfying Differential Equations

Abstract Views: 271  |  PDF Views: 0

Authors

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

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.