Orthorecursive expansion of unity
| Autor: | Alexander Kalmynin, Petr Kosenko |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Sequence
Algebra and Number Theory Recurrence relation Mathematics - Number Theory Computer Science::Information Retrieval Astrophysics::Instrumentation and Methods for Astrophysics Hilbert space Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Combinatorics symbols.namesake TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES FOS: Mathematics ComputingMethodologies_DOCUMENTANDTEXTPROCESSING symbols Computer Science::General Literature Harmonic number Number Theory (math.NT) ComputingMilieux_MISCELLANEOUS Mathematics |
| Popis: | We study the properties of a sequence cn defined by the recursive relation \[\frac{c_0}{n + 1}+\frac{c_1}{n + 2}+\ldots+\frac{c_n}{2n + 1}=0\] for $n>1$ and $c_0=1$. This sequence also has an alternative definition in terms of certain norm minimization in the space $L^2([0, 1])$. We prove estimates on growth order of $c_n$ and the sequence of its partial sums, infinite series identities, connecting $c_n$ with harmonic numbers $H_n$ and also formulate some conjectures based on numerical computations. 17 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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