Results 11 to 20 of about 347 (43)
Two closed forms for the Bernoulli polynomials [PDF]
, 2015 In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 ...
Chapman, Robin J., Qi, Feng
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Explicit Formulas involving q-Euler Numbers and Polynomials [PDF]
, 2012 In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator.
Acikgoz, Mehmet +2 more
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Diagonal recurrence relations for the Stirling numbers of the first kind [PDF]
, 2015 In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.Comment: 7 ...
Qi, Feng
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I [PDF]
, 2010 In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations are useful to
Dil, Ayhan, Kurt, Veli
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Sums of Powers and Special Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their ...
Boyadzhiev Khristo N.
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An explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind [PDF]
, 2014 In the paper, the author finds an explicit formula for computing Bernoulli numbers of the second kind in terms of Stirling numbers of the first kind.Comment: 5 ...
Qi, Feng
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SOME REMARKS ABOUT STIRLING NUMBERS OF THE SECOND KIND
Human Research in Rehabilitation, 2013 In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas.
Ramiz Vugdalić, Fatih Destović
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, 2012 In the paper, the author establishes some identities which show that the functions $\frac1{(1-e^{\pm t})^k}$ and the derivatives $\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$ can be expressed each other by linear combinations with coefficients involving the ...
Andrews +5 more
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Fourier series of functions involving higher-order ordered Bell polynomials
Open Mathematics, 2017 In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the ...
Kim Taekyun +3 more
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