Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials. (English) Zbl 1427.11023
Summary: In the paper, the authors establish by two approaches several explicit formulas for special values of the Bell polynomials of the second kind, derive explicit formulas for the Euler numbers and polynomials in terms of double sums and the weighted Stirling numbers, and find a property for special values of the Bell polynomials of the second kind.
MSC:
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 11B73 | Bell and Stirling numbers |
| 12E10 | Special polynomials in general fields |
| 33B10 | Exponential and trigonometric functions |
Keywords:
explicit formula; special value; Bell polynomial of the second kind; Euler number; Euler polynomial; double sum; weighted Stirling number; propertyReferences:
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