[PDF] Top 20 Sums of Products of Euler Polynomials and Numbers
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Sums of Products of Euler Polynomials and Numbers
... corresponding analysis a particular case of so-called non-Archimedean analysis. He showed that many problems of the description of reality with the aid of real numbers are induced by unlimited application of the ... See full document
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Remarks on Sum of Products of Twisted Euler Polynomials and Numbers
... and Euler numbers and polynomials were studied by many au- thors see for details ...Bernoulli numbers and polynomi- ...complete sums of products of h, q-extension of higher-order ... See full document
8
Sums of products of the degenerate Euler numbers
... for sums of products of the degenerate Euler polynomials and the degenerate Bernoulli ...degenerate Euler polynomials, an expression can be obtained for ... See full document
7
Sums of products of Apostol Bernoulli and Apostol Euler polynomials
... Apostol-Euler polynomials and numbers is performed. Some closed formulae of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and ... See full document
13
Sums of products of two reciprocal Fibonacci numbers
... the sums and alternating sums of the products of two recipro- cal Fibonacci numbers in various ...alternating sums can be applied to study other types of alternating sums, which ... See full document
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New formulae of products of the Frobenius Euler polynomials
... Bernoulli numbers and Euler numbers, respectively. These numbers and polynomials play important roles in many different areas of mathematics including number theory, combinatorics, ... See full document
13
Ordinary and degenerate Euler numbers and polynomials
... power sums can be expressed in terms of some values of Euler ...on Euler numbers and polynomials, and those on degenerate Euler numbers and polynomials, which are ... See full document
11
SOME COMPUTATIONS BETWEEN SUMS OF POWERS OF CONSECUTIVE INTEGERS AND ALTERNATING SUMS OF POWERS OF CONSECUTIVE INTEGERS
... Bernoulli, Euler and Genocchi polynomials and numbers and its generalizations have been extensively studied and investigated by many mathematicians and physicists (see ...Genocchi polynomials ... See full document
6
Sums of finite products of Legendre and Laguerre polynomials
... In this paper, we considered the Fourier series expansions for functions associated with Legendre and Laguerre polynomials. In addition, by using a method other than Fourier series expansions, we were able to ... See full document
17
Euler Basis, Identities, and Their Applications
... Ryoo, “Some relations between twisted q-Euler numbers and Bernstein polynomials,” Advanced Studies in Contemporary Mathematics, vol.. Simsek, “Complete sum of products of h, q-extension [r] ... See full document
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The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked
... by Euler [7], a researcher working with the Ber- noulli brothers at ...[8], Euler had followed de Moivre in given B k the denomination Bernoulli numbers, introduced the ... See full document
13
On the Fermionic adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials
... Research Article On the Fermionic p-adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials T.. Division of General Education-Mathematics, Kwa[r] ... See full document
12
Special Numbers on Analytic Functions
... Stirling numbers of the first and the second are used in pure and applied ...These numbers occur in combinatorics and in the theory of ...Stirling numbers of the second kind S n v ( ) , are defined ... See full document
8
Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
... 1.3. Derivative polynomials. Suppose f is a function whose derivative is a poly- nomial in f , that is, f 0 (x) = P (f (x)) for some polynomial P . Then all the higher order derivatives of f are also ... See full document
12
Identities, inequalities for Boole type polynomials: approach to generating functions and infinite series
... combinatorial numbers and polynomials, and for Peters type polynomials with the help of their generating ...special numbers and polynomials such as Stirling numbers, the ... See full document
11
Some Relationships between the Analogs of Euler Numbers and Polynomials
... q-Euler numbers and ...q-Euler numbers and gener- alized twisted q-Euler numbers, ...of Euler numbers, which is ... See full document
22
Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials
... consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with ...those sums ... See full document
14
Identities on the Bernoulli and Genocchi Numbers and Polynomials
... Ryoo, “On the fermionic p-adic integral representation of Bernstein polynomials associated with Euler numbers and polynomials,” Journal of Inequalities and Applications, vol... Operation[r] ... See full document
10
New Type of Degenerate Poly-Frobenius-Euler Polynomials and Numbers
... Bernoulli polynomials by means of the degenerate polylogarithm ...poly-Frobenius-Euler polynomials, called the new type of degenerate poly-Frobenius-Euler polynomials, by means of the ... See full document
11
Some new identities of Frobenius Euler numbers and polynomials
... In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, several authors have studied some identities of Frobenius-Euler polynomials. ... See full document
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