Geodesic
A Note on Completely and Absolutely Monotone Functions
Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 143-148

Voir la notice de l'article provenant de la source Cambridge University Press

The solutions of a certain class of first order linear differential equations are shown to be either completely or absolutely monotone depending on the nature of its coefficients. This is a simple theorem which is used to deduce a number of new and interesting results dealing with the complete and absolute monotonicity of functions. In particular, a partial answer is supplied to a question posed by Askey and Pollard: “When is completely monotone?”
DOI : 10.4153/CMB-1982-020-x
Mots-clés : 26D15, 34A10, 33A15, 33A40, Completely monotone, absolutely monotone, Inequalities, Bessel functions, gamma functions 
Mahajan, Arvind; Ross, Dieter K. A Note on Completely and Absolutely Monotone Functions. Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 143-148. doi: 10.4153/CMB-1982-020-x
@article{10_4153_CMB_1982_020_x,
     author = {Mahajan, Arvind and Ross, Dieter K.},
     title = {A {Note} on {Completely} and {Absolutely} {Monotone} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {143--148},
     year = {1982},
     volume = {25},
     number = {2},
     doi = {10.4153/CMB-1982-020-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-020-x/}
}
TY  - JOUR
AU  - Mahajan, Arvind
AU  - Ross, Dieter K.
TI  - A Note on Completely and Absolutely Monotone Functions
JO  - Canadian mathematical bulletin
PY  - 1982
SP  - 143
EP  - 148
VL  - 25
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-020-x/
DO  - 10.4153/CMB-1982-020-x
ID  - 10_4153_CMB_1982_020_x
ER  - 
%0 Journal Article
%A Mahajan, Arvind
%A Ross, Dieter K.
%T A Note on Completely and Absolutely Monotone Functions
%J Canadian mathematical bulletin
%D 1982
%P 143-148
%V 25
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-020-x/
%R 10.4153/CMB-1982-020-x
%F 10_4153_CMB_1982_020_x

[1] 1. Askey, R., Summability of Jacobi series, Trans. Amer. Math. Soc. 179 (1973), pp. 71-84. Google Scholar

[2] 2. Askey, R.. and Pollard, H., Some absolutely monotonie and completely monotonie functions, SIAM J. Math. Anal. 5 (1974), pp. 58-63. Google Scholar

[3] 3. Fields, J. L. and Ismail, M., On some conjectures of Askey concerning completely monotonie functions, Spline Functions and Approximation Theory, edited by Meir, A. and Sharma, A., ISNM Vol. 21, Birkhauser Verlag, Basel, 1973, pp. 101-111. Google Scholar

[4] 4. Fields, J. L. and Ismail, M. E.-H., On the positivity of some F's, SIAM J. Math. Anal., 6 (1975), pp. 551-559. Google Scholar

[5] 5. Gasper, G., Nonnegative sums of cosine, ultraspherical and Jacobi polynomials, J. Math. Anal. Appl. 26 (1969), pp. 60-68. Google Scholar

[6] 6. Muldoon, M. E., Some monotonicity properties and characterisations of the gamma function, Aequationes Math. 18 (1978), pp. 54-63. Google Scholar

[7] 7. Watson, G. N., A treatise on the theory of Bessel functions, Cambridge Univ. Press, 1966. Google Scholar

[8] 8. Widder, D. V., Laplace Transforms, Princeton University Press, Princeton, N.J., 1946. Google Scholar

Cité par Sources :