In this talk, we deal with Vieta-Lucas wavelets. In particular, we discuss the differentiability of Vieta-Lucas wavelets. We use this wavelet family to reconstruct a function by the introduction of connection coefficients. Moreover, we compare Vieta-Lucas wavelets and Chebyshev wavelets together with their main applications. Finally, we give an application in fractional calculus.

References:
[1] Chalice, D. A characterization of the Cantor function, Am. Math. Mon. 1991, 98(3), 255-258.
[2] Guariglia, E.; Guido, R.C. Chebyshev wavelet analysis. J. Funct. Spaces 2022, 2022(1), Art. No. 5542054.
[3] Horadam, A.F. Vieta Polynomials. Fibonacci Quart. 2002, 40(3), 223-232.
[4] Prodinger, H. Representing derivatives of Chebyshev polynomials by Chebyshev polynomials and related questions. Open Math. 2017, 15(1), 1156-1160.
[5] Tasci, D.; Yalcin, F. Vieta-Pell and Vieta-Pell-Lucas polynomials. Adv. Differ. Equ. 2013, 2013(1), Art. No. 224.