References

THE INVERSE TAYLOR OPERATOR AND COMPLETELY MONOTONIC FUNCTIONS


[1] H. Alzer and C. Berg, Some classes of completely monotonic functions, Ann. Acad. Scient. Fennicae 27 (2002), 445-460.

[2] C. Berg and H. L. Pederson, A completely monotone function related to the gamma function, J. Comp, Appl. Math. 133 (2001), 219-230.

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

[4] W. Feller, Completely monotone functions and sequences, Duke Math. J. 5 (1939), 661-674.

[5] H. van Haeringen, Completely monotonic and related functions, J. Math. Anal. Appl. 204 (1996), 389-408.

[6] M. E. H. Ismail, Integral representations and complete monotonicity of various quotients of Bessel functions, Canad. J. Math. 29 (1977), 1198-1207.

[7] M. E. H. Ismail, Complete monotonicity of modified Bessel functions, Proc. Amer. Math. Soc. 108 (1990), 353-361.

[8] 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 (2013).

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

[10] D. P. Kanoussis and V. G. Papanicolaou, New expansions of two trigonometric functions, Journal of Concrete and Applied Mathematics 12(3-4) (2014), 331.

[11] W. Krull, Bemerkungen zur Differezengleichung Math. Nachr. 1 (1948), 365-376.

[12] M. Kuczma, O Rownaniu Funkcyjnym Zeszyty Naukowe Univ. Jagiell., Mat.- Fiz.- Chem. 4 (1958), 27-38.

[13] K. S. Miller and S. G. Samco, Completely monotonic functions, Integr. Transf. and Special Functions 12(4) (2001), 389-402.

[14] D. V. Widder, The Laplace Transform, Princeton Univ. Press, Princeton, N.J., 1941.