# Polynomially Interpolated Legendre Multiplier Sequences

Polynomially Interpolated Legendre Multiplier Sequences We prove that if a multiplier sequence for the Legendre basis can be interpolated by a polynomial, then the polynomial must have the form $$\{h(k^2+k)\}_{k=0}^{\infty }$$ { h ( k 2 + k ) } k = 0 ∞ , where $$h\in \mathbb {R}[x]$$ h ∈ R [ x ] . We also show that a non-trivial collection of polynomials of a certain form interpolate multiplier sequences for the Legendre basis, and we state conjectures on how to extend these results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

# Polynomially Interpolated Legendre Multiplier Sequences

, Volume 18 (2) – Nov 28, 2017
19 pages

/lp/springer-journals/polynomially-interpolated-legendre-multiplier-sequences-i3Op0ywPdi
Publisher
Springer Journals
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-017-0221-3
Publisher site
See Article on Publisher Site

### Abstract

We prove that if a multiplier sequence for the Legendre basis can be interpolated by a polynomial, then the polynomial must have the form $$\{h(k^2+k)\}_{k=0}^{\infty }$$ { h ( k 2 + k ) } k = 0 ∞ , where $$h\in \mathbb {R}[x]$$ h ∈ R [ x ] . We also show that a non-trivial collection of polynomials of a certain form interpolate multiplier sequences for the Legendre basis, and we state conjectures on how to extend these results.

### Journal

Computational Methods and Function TheorySpringer Journals

Published: Nov 28, 2017

### References

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