Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup>
This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connectio...
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2025-01-01
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| Series: | Mathematics |
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| author | Feng Qi |
| author_facet | Feng Qi |
| author_sort | Feng Qi |
| collection | DOAJ |
| description | This paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central factorial numbers, the Stirling numbers, and specific matrix inverses, and derives several closed-form formulas and inequalities. Additionally, this paper reveals new insights into the properties of these mathematical objects, including logarithmic convexity, explicit expressions for certain quantities, and identities involving the Bell polynomials of the second kind. |
| format | Article |
| id | doaj-art-1aa159e6d16d486ab23aa8fea3e26c47 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-1aa159e6d16d486ab23aa8fea3e26c472025-01-24T13:39:48ZengMDPI AGMathematics2227-73902025-01-0113222310.3390/math13020223Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup>Feng Qi0School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, ChinaThis paper presents an extensive investigation into several interrelated topics in mathematical analysis and number theory. The author revisits and builds upon known results regarding the Maclaurin power series expansions for a variety of functions and their normalized remainders, explores connections among central factorial numbers, the Stirling numbers, and specific matrix inverses, and derives several closed-form formulas and inequalities. Additionally, this paper reveals new insights into the properties of these mathematical objects, including logarithmic convexity, explicit expressions for certain quantities, and identities involving the Bell polynomials of the second kind.https://www.mdpi.com/2227-7390/13/2/223Vandermonde matrixinverse matrixStirling numberMaclaurin power series expansionnormalized remaindercentral factorial number |
| spellingShingle | Feng Qi Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup> Mathematics Vandermonde matrix inverse matrix Stirling number Maclaurin power series expansion normalized remainder central factorial number |
| title | Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup> |
| title_full | Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup> |
| title_fullStr | Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup> |
| title_full_unstemmed | Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup> |
| title_short | Series and Connections Among Central Factorial Numbers, Stirling Numbers, Inverse of Vandermonde Matrix, and Normalized Remainders of Maclaurin Series Expansions <sup>†</sup> |
| title_sort | series and connections among central factorial numbers stirling numbers inverse of vandermonde matrix and normalized remainders of maclaurin series expansions sup † sup |
| topic | Vandermonde matrix inverse matrix Stirling number Maclaurin power series expansion normalized remainder central factorial number |
| url | https://www.mdpi.com/2227-7390/13/2/223 |
| work_keys_str_mv | AT fengqi seriesandconnectionsamongcentralfactorialnumbersstirlingnumbersinverseofvandermondematrixandnormalizedremaindersofmaclaurinseriesexpansionssupsup |