# Exponential Polynomials, Stirling Numbers, and Evaluation of Some Gamma Integrals

## Related Articles

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Abstract. We construct the new q-extension of Bernoulli numbers and polynomials in this paper. From these new q-extension of Bernoulli numbers and polynomials, the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to ? will be also derived by p-adic invariant...

- Old and New Identities for Bernoulli Polynomials via Fourier Series. Navas, Luis M.; Ruiz, Francisco J.; Varona, Juan L. // International Journal of Mathematics & Mathematical Sciences;2012, p1
The Bernoulli polynomials Bk restricted to [0, 1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0, 1) are linear combinations of terms of the form 1/nk. If we can make this linear...

- Fourier Series of the Periodic Bernoulli and Euler Functions. Cheon Seoung Ryoo; Hyuck In Kwon; Jihee Yoon; Yu Seon Jang // Abstract & Applied Analysis;2014, p1
We give some properties of the periodic Bernoulli functions and study the Fourier series of the periodic Euler functions which are derived periodic functions from the Euler polynomials. And we derive the relations between the periodic Bernoulli functions and those from Euler polynomials by using...

- Approximation of classes of convolutions by linear operators of special form. Zastavnyi, V.; Savchuk, V. // Mathematical Notes;Oct2011, Vol. 90 Issue 3/4, p333
A parametric family of operators G is constructed for the class of convolutions W( K) whose kernel K was generated by the moment sequence. We obtain a formula for evaluating . For the case in which W( K)= W, we obtain an expansion in powers of the parameter É›=âˆ’ln Ï for E( W; G),...

- SOME IDENTITIES OF THE GENERALIZED TWISTED BERNOULLI NUMBERS AND POLYNOMIALS OF HIGHER ORDER. Seog-Hoon Rim; Young-Hee Kim; Byungje Lee; Taekyun Kim // Journal of Computational Analysis & Applications;Jul2010, Vol. 12 Issue 3, p695
The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to x from the properties of the p-adic invariant integral. We give some interesting identities for the power sums and the generalized twisted Bernoulli...

- Closed-form summation of the Dowker and related sums. Cvijovic, Djurdje; Srivastava, H. M. // Journal of Mathematical Physics;Apr2007, Vol. 48 Issue 4, p043507
Finite sums of powers of cosecants appear in a wide range of physical problems. We, through a unified approach which uses contour integrals and residues, establish the summation formulas for two general families of such sums. One of them is the family which was first studied and summed in closed...

- On the weighted q-Bernstein polynomials associated with the twisted q-Bernoulli numbers. Kim, T.; Lee, B.; Ryoo, C. S. // Journal of Computational Analysis & Applications;Jul2012, Vol. 14 Issue 5, p842
Recently, Kim introduced q-Bernstein polynomials and weighted q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips(see [6]). In this paper we investigate some properties on the weighted q-Bernstein polynomials. From these properties, we derive some interesting new...

- ASYMPTOTIC ANALYSIS OF THE NÃ–RLUND AND STIRLING POLYNOMIALS. Ward, Mark Daniel // Applicable Analysis & Discrete Mathematics;2012, Vol. 6 Issue 1, p95
We provide a full asymptotic analysis of the NÃ¶rlund polynomials and Stirling polynomials. We give a general asymptotic expansion-to any desired degree of accuracy-when the parameter is not an integer. We use singularity analysis, Hankel contours, and transfer theory. This investigation was...

- Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials. Taekyun Kim; Seog-Hoon Rim; Byungje Lee // Abstract & Applied Analysis;2009, Special section p1
By the properties of p-adic invariant integral on Zp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on Zp, we give some interesting relationship between the power sums and the generalized...