Jacob's ladders and new orthogonal systems generated by Jacobi polynomials

2010/10/18 by Jan Moser, Moser, Jan
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1010.3540

openalex publication_date 2010/10/18 · arxiv created 2010/11/18 · arxiv updated 2010/11/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Is is shown in this paper that there is a connection between the Riemann zeta-function \zf and the classical Jacobi's polynomials, i.e. the Legendre polynomials, Chebyshev polynomials of the first and the second kind,...

Citations

• Jacob's ladders and the first asymptotic formula for the expression of the fifth order Z³[...]Z²(t) for the collection of disconnected sets
• Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral

Related

• Jacob's ladder as generator of new class of iterated L₂-orthogonal systems and their dependence on the Riemann's function
• Jacob's ladders, reverse iterations and new infinite set of L₂-orthogonal systems generated by the Riemann \zf-function
• Jacob's ladders and vector operator producing new generations of L₂-orthogonal systems connected with the Riemann's ζ(\frac 12+it) function
• Jacob's ladders, ζ-transformation of the Fourier orthogonal system (2014) and new infinite sets of ζ-equivalents of the Fermat-Wiles theorem
• Jacob's ladders, interactions between ζ-oscillating systems and ζ-analogue of an elementary trigonometric identity