Applications of Apostol-type Numbers and Polynomials: Approach to Techniques of Computation Algorithms in Approximation and Interpolation Functions

Şimşek, Yılmaz

doi:10.1007/978-3-030-84122-5_40

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2022

2023

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“…where 𝑘 ∈ ℕ and 𝜗 ∈ ℂ. The numbers 𝐸 𝑟 * (−𝑘) (𝜗) are called the second kind Apostol type Euler numbers of order -𝑘 (Simsek, 2017;2018;2022a).…”

Section: Introductionmentioning

confidence: 99%

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Certain Finite Sums Pertaining to Leibnitz, Harmonic and Other Special Numbers

Kilar¹

2022

Gazi University Journal of Science Part A: Engineering and Innovation

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The present manuscript deals with some certain finite sums and identities pertaining to some special numbers. Using generating functions methods, some relations and identities involving the Apostol type Euler and combinatorial numbers, and also the Fubini type numbers and polynomials, are given. Then, by using some certain classes of special finite sums involving the following rational sum which is defined by Simsek (2021b): y(r,ϑ)=∑_(b=0)^r▒〖(-1)^r/((1+b) ϑ^(b+1) 〖(ϑ-1)〗^(r-b+1) ),〗many new certain finite sums and formulas related to the Leibnitz, Harmonic, Changhee, and Daehee numbers are obtained. Moreover, some applications of these results are presented.

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“…where 𝑘 ∈ ℕ and 𝜗 ∈ ℂ. The numbers 𝐸 𝑟 * (−𝑘) (𝜗) are called the second kind Apostol type Euler numbers of order -𝑘 (Simsek, 2017;2018;2022a).…”

Section: Introductionmentioning

confidence: 99%

“…where 𝑘 ∈ ℕ and 𝜗 ∈ ℂ (Simsek, 2017;2018;2022a; see also Kucukoglu & Simsek, 2018;Kucukoglu et al, 2019).…”

Section: Introductionmentioning

confidence: 99%