A series transformation formula and related polynomials

International Journal of Mathematics and Mathematical Sciences

Volumn 2005, Issue 23, 2005, Pages 3849-3866

  Boyadzhiev, Khristo N ^a  

^a NONE

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EID: 33746689720     PISSN: 01611712     EISSN: 16870425     Source Type: Journal    
DOI: 10.1155/IJMMS.2005.3849     Document Type: Article

References (37)

1. R. Ayoub Euler and the zeta function Amer. Math. Monthly The American Mathematical Monthly 81 10 1974 1067 1086
2. E. T. Bell Exponential numbers Amer. Math. Monthly 41 1934 411 419
3. E. T. Bell Exponential polynomials Ann. of Math. (2) Annals of Mathematics. Second Series 35 1934 2 258 277
4. B. C. Berndt Ramanujan's Notebooks. Part I Springer New York 1985
5. P. L. Butzer A. A. Kilbas J. J. Trujillo Compositions of Hadamard-type fractional integration operators and the semigroup property J. Math. Anal. Appl. Journal of Mathematical Analysis and Applications 269 2002 2 387 400
6. P. L. Butzer A. A. Kilbas J. J. Trujillo Fractional calculus in the Mellin setting and Hadamard-type fractional integrals J. Math. Anal. Appl. Journal of Mathematical Analysis and Applications 269 2002 1 1 27
7. P. L. Butzer A. A. Kilbas J. J. Trujillo Mellin transform analysis and integration by parts for Hadamard-type fractional integrals J. Math. Anal. Appl. Journal of Mathematical Analysis and Applications 270 2002 1 1 15
8. L. Comtet Advanced Combinatorics D. Reidel Dordrecht 1974
9. M. E. Dasef S. M. Kautz Some sums of some importance College Math. J. 28 1997 52 55
10. N. G. de Bruijn Asymptotic Methods in Analysis Dover New York 1981
11. A. Erdélyi Higher Transcendental Functions 1 McGrow-Hill New York 1955
12. C. Ferreira J. L. López Asymptotic expansions of the Hurwitz-Lerch zeta function J. Math. Anal. Appl. Journal of Mathematical Analysis and Applications 298 2004 1 210 224
13. H. W. Gould Euler's formula for n th differences of powers Amer. Math. Monthly The American Mathematical Monthly 85 1978 6 450 467
14. R. L. Graham D. E. Knuth O. Patashnik Concrete Mathematics Addison-Wesley Massachusetts 1994
15. G. H. Hardy On the zeros of certain classes of integral Taylor series Proc. London Math. Soc. (2) 2 1905 401 431, Part II
16. G. H. Hardy Collected Papers of G. H. Hardy (including joint papers with J. E. Littlewood and others). Vol. IV Clarendon Press Oxford 1969 ix+722 pp. (1 plate)
17. L. C. Hsu P. J.-S. Shiue On certain summation problems and generalizations of Eulerian polynomials and numbers Discrete Math. Discrete Mathematics 204 1999 1-3 237 247
18. J. Klippert Summing power series with polynomial coefficients Amer. Math. Monthly 90 1983 4 284 285
19. n and its application to series Math. Mag. 76 2003 5 364 371
20. D. E. Knuth Two notes on notation Amer. Math. Monthly The American Mathematical Monthly 99 1992 5 403 422
21. H. K. Krishnapriyan Eulerian polynomials and Faulhaber's result on sums of powers of integers College Math. J. 26 1995 3 119 123
22. L. Lovász Combinatorial Problems and Exercises North-Holland Amsterdam 2nd 1993
23. F. W. J. Olver Asymptotics and Special Functions Academic Press New York 1974
24. J. Riordan Combinatorial Identities John Wiley & Sons New York 1968
25. G.-C. Rota Finite Operator Calculus Academic Press New York 1975
26. I. J. Schwatt An Introduction to the Operations with Series Chelsea New York 1924
27. J. Touchard Proprietes arithmetiques de certains nombres recurrents Ann. Soc. Sci. Bruxelles A 53 1933 21 31 French
28. J. Touchard Nombres exponentiels et nombres de Bernoulli Canad. J. Math. Canadian Journal of Mathematics. Journal Canadien de Mathématiques 8 1956 305 320 French
29. I. Vardi Determinants of Laplacians and multiple gamma functions SIAM J. Math. Anal. SIAM Journal on Mathematical Analysis 19 1988 2 493 507
30. X. Wang L. C. Hsu A summation formula for power series using Eulerian fractions Fibonacci Quart. The Fibonacci Quarterly. The Official Journal of the Fibonacci Association 41 2003 1 23 30
31. E. W. Weisstein Bell Numbers from MathWorld, http://mathworld.wolfram.com/BellNumber.html
32. E. W. Weisstein Eulerian Numbers from MathWorld, http://mathworld.wolfram.com/EulerianNumber.html
33. E. W. Weisstein Exponential Polynomial from MathWorld, http://mathworld.wolfram.com/ExponentialPolynomial.html
34. E. W. Weisstein Stirling Numbers of the First Kind from MathWorld, http://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html
35. E. W. Weisstein Stirling Numbers of the Second Kind from MathWorld, http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
36. E. T. Whittaker G. N. Watson A Course in Modern Analysis 4th Cambridge University Press Cambridge 1927
37. Problem 11007 Amer. Math. Monthly, textbf{110} (2003), no. 4