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Application: Bernoulli Polynomials and Power Sums

The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked

The Powers Sums, Bernoulli Numbers, Bernoulli Polynomials Rethinked

... a power sum has a meaning and is exactly equal to the Bernoulli poly- nomial of the same ...powers sums in term of sums of successive derivatives of Bernoulli polynomi- al multiplied ...

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On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials

On the Symmetric Properties for the Generalized Twisted Bernoulli Polynomials

... twisted Bernoulli polynomials and ...the power sums and the generalized twisted Bernoulli polynomials using the symmetric properties for the p-adic invariant ...

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Sums of products of Apostol Bernoulli and Apostol Euler polynomials

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 numbers are established by ...

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Certain combinatoric Bernoulli polynomials and convolution sums of divisor functions

Certain combinatoric Bernoulli polynomials and convolution sums of divisor functions

... convolution sums and their ap- plications is classical, and they play an important role in number ...combinatorial Bernoulli numbers and convolution ...

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A New Approach to  Bernoulli Numbers and  Bernoulli Polynomials Related to  Bernstein Polynomials

A New Approach to Bernoulli Numbers and Bernoulli Polynomials Related to Bernstein Polynomials

... 11 T. Kim, “Non-Archimedean q-integrals associated with multiple Changhee q-Bernoulli polynomials,” Russian Journal of Mathematical Physics, vol. 10, no. 1, pp. 91–98, 2003. 12 T. Kim, “Power series ...

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10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums

10. Some series identities for some special classes of Apostol-Bernoulli and Apostol-Euler polynomials related to generalized power and alternating sums

... Abstract. The purpose of this paper is to obtain several series identities in- volving some classes of generalized Apostol-Bernoulli and Apostol-Euler poly- nomials introduced lately by Srivastava et al. in [16, ...

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Sums of finite products of Bernoulli functions

Sums of finite products of Bernoulli functions

... 8. Miki, H: A relation between Bernoulli numbers. J. Number Theory 10(3), 297-302 (1978) 9. Srivastava, HM: Some generalizations and basic extensions of the Bernoulli, Euler and Genocchi polynomials. ...

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q Bernoulli numbers and q Bernoulli polynomials revisited

q Bernoulli numbers and q Bernoulli polynomials revisited

... 2. Kim, T: On p-adic q-L-functions and sums of powers. Discrete Math. 252, 179 – 187 (2002). doi:10.1016/S0012-365X(01) 00293-X 3. Ryoo, CS: A note on the weighted q -Euler numbers and polynomials. Adv. ...

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Congruences for Generalized  Bernoulli Polynomials

Congruences for Generalized Bernoulli Polynomials

... Note that there exist φp ∗ distinct solutions, modulo p ∗ , to the equation x φp ∗ − 1 0, and each solution must be congruent to one of the values a ∈ Z, where 1 ≤ a ≤ p ∗ − 1, a, p 1. Thus, by Hensel’s lemma, given a ∈ ...

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A note on the Generalized Bernoulli and Euler Polynomials

A note on the Generalized Bernoulli and Euler Polynomials

... generalized Bernoulli and generalized Euler ...Appell polynomials as- sociated with uniformly distributed and Bernoulli distributed random variables and their ...

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A note on higher order Bernoulli polynomials

A note on higher order Bernoulli polynomials

... 13. Kim, T: Some formulae for the q-Bernstein polynomials and q-deformed binomial distributions. J. Comput. Anal. Appl. 14(5), 917-933 (2012) 14. Petojevi´c, A: New sums of products of Bernoulli ...

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Identities on the Bernoulli and Genocchi Numbers and Polynomials

Identities on the Bernoulli and Genocchi Numbers and Polynomials

... for Bernoulli and Euler polynomials,” Journal of Di ff erence Equations and Applications, ...of power sum polynomials and multivariate fermionic p-adic invariant integral on Z p ,” Russian ...

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Sums of Products of  Euler Polynomials and Numbers

Sums of Products of Euler Polynomials and Numbers

... tried to build a p-adic picture of reality based on the field of p-adic numbers Q p and corresponding analysis a particular case of so-called non-Archimedean analysis. He showed that many problems of the description of ...

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Series of sums of products of higher order Bernoulli functions

Series of sums of products of higher order Bernoulli functions

... 1. Bayad, A, Kim, T: Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials. Russ. J. Math. Phys. 18(2), 133-143 (2011) 2. Kim, DS, Kim, T: A note on higher-order Bernoulli ...

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Higher order Bernoulli, Euler and Hermite polynomials

Higher order Bernoulli, Euler and Hermite polynomials

... 5. Carlitz, L: A note on q-Eulerian numbers. J. Comb. Theory, Ser. A 25(1), 90-94 (1978) 6. Cangul, IN, Simsek, Y: A note on interpolation functions of the Frobenius-Euler numbers. In: Application of Mathematics ...

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New approach to twisted q Bernoulli polynomials

New approach to twisted q Bernoulli polynomials

... of power sum polynomials and multivariate fermionic p-adic invariant integral on Z p ...On sums of products of the extended q-Euler ...twisted Bernoulli numbers and polynomials ...

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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials

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 of ...

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Some identities on Bernoulli and Euler polynomials arising from orthogonality of Legendre polynomials

Some identities on Bernoulli and Euler polynomials arising from orthogonality of Legendre polynomials

... 7. Carlitz, L: Congruence properties of the polynomials of Hermite, Laguerre and Legendre. Math. Z. 59, 474-483 (1954) 8. Ding, D, Yang, J: Some identities related to the Apostol-Euler and Apostol-Bernoulli ...

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Some identities on Bernoulli and Euler polynomials arising from the orthogonality of Laguerre polynomials

Some identities on Bernoulli and Euler polynomials arising from the orthogonality of Laguerre polynomials

... q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Z p ...of power sum polynomials and multivariate fermionic p-adic invariant integral on Z p ...

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Sums of finite products of Legendre and Laguerre polynomials

Sums of finite products of Legendre and Laguerre polynomials

... study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with ...those sums of finite products as linear combinations of ...

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