A Note on the (ℎ,𝑞)-Extension of Bernoulli Numbers and Bernoulli Polynomials
We observe the behavior of roots of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). The main purpose of this paper is also to investi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/807176 |
| Summary: | We observe the behavior of roots of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). The main purpose of this paper is also to investigate
the zeros of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). Furthermore, we give a table for the zeros of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). |
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| ISSN: | 1026-0226 1607-887X |