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2025
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| Online Access: | https://doi.org/10.5281/zenodo.15856214 |
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| _version_ | 1866902221547896832 |
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| author | Robert, Polak |
| author_facet | Robert, Polak |
| contents | <p>This note introduces a new class of "central Bernoulli numbers", denoted C_r(n), which arise naturally from the cascade coefficients of the Moment-Centred Decomposition (MVDC) method. It provides a proof that these numbers can be expressed in a closed form using Nörlund's generalised Bernoulli polynomials. A compact exponential generating function for C_r(n) is derived, and their relationship to the classical Bernoulli numbers is shown in the n→∞ limit. The paper serves as a self-contained analytic appendix to the main MVDC paper, anchoring the method in the classical theory of special polynomials.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15856214 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Central (C-)Bernoulli Numbers Arising from the MVDC Method Robert, Polak <p>This note introduces a new class of "central Bernoulli numbers", denoted C_r(n), which arise naturally from the cascade coefficients of the Moment-Centred Decomposition (MVDC) method. It provides a proof that these numbers can be expressed in a closed form using Nörlund's generalised Bernoulli polynomials. A compact exponential generating function for C_r(n) is derived, and their relationship to the classical Bernoulli numbers is shown in the n→∞ limit. The paper serves as a self-contained analytic appendix to the main MVDC paper, anchoring the method in the classical theory of special polynomials.</p> |
| title | Central (C-)Bernoulli Numbers Arising from the MVDC Method |
| url | https://doi.org/10.5281/zenodo.15856214 |