References

A BERNOULLI TYPE EXPANSION OF THE INVERSE TAYLOR OPERATOR, AND SOME OF ITS APPLICATIONS


[1] M. Abramowitz and C. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, New York, Dover.

[2] A. Beardon, Sums of powers of integers, Amer. Math. Monthly 103 (1996), 201-213.

[3] G. F. C. de Bryun and M. de Villiers, Formulas for The Fibonacci Quarterly 32(3) (1994), 271-276.

[4] J. Dufresnoy and Ch. Pisot, Sur la relation functionnelle Bull. Soc. Math. Belgique 15 (1963), 259-270.

[5] D. P. Kanoussis and V. G. Papanicolaou, The R-transform of a real-valued function and some of its applications, Journal of Applied Functional Analysis 8(3-4) (2013), 301-316.

[6] D. P. Kanoussis and V. G. Papanicolaou, On the inverse of the Taylor operator, Scientia, Series A, Mathematical Sciences 24 (2013), 55-66.

[7] W. Krull, Bemerkungen zur Differezengleichung Math. Nachr. 1 (1948), 365-375.

[8] M. Kuczma, O rownaniu funkcyjnym Zeszyty Naukowe Uniw. Jagiell., Mat.-Fiz.-Chem. 4 (1958), 27-38.

[9] M. Merkle and M. M. R. Merkle, Krull’s theory for the double gamma function, Appl. Math. Comput. 218 (2011), 935-943.

[10] R. Owens, Sums of powers of integers, Mathematics Magazine 65 (1992), 38-40.