Site Loader
Rock Street, San Francisco

In this study, we establish some new inequalities for Tricomi, Bessel and modified Bessel functions. Some special and confluent cases of our main aim are established with the help of the inequalities for hypergeometric functions $;_{0}F_{1}ig{(}-;c;zig{)}$, $c>0$.Inequalities for special functions appear infrequently in the literature. A good number of such inequalities are motivated by different problems in mathematics, sciences and engineering that involve inequalities for special functions in cite{Bi2, bo, bu, ca, erb, la3, lu2, lu3, lu4, ro, ro1, ro2} for the theory and numerous examples and references. Joshi and Arya cite{ja2, ja4} are devoted to analogous questions. Recently, Joshi and Bissu cite{jb1, jb3} introduced the concept of the inequalities for confluent hypergeometric function. The inequalities of Bessel functions of the first kind are important in several problems of applied mathematics, mathematical physics and engineering sciences. Because of their importance, there is an extensive literature on various properties of the inequalities of Bessel functions of the first kind, and they were investigated by famous researchers such as Watson cite{wa1}, Joshi and Bissu cite{jb3}, Joshi and Bissu cite{jb1}, Laforgia cite{la1, la2}, Nasell cite{na}. For more details, the author has earlier introduced the inequalities for special functions in the papers cite{sh1, sh2}.Our main motivation for this paper is to complement and improve the results of Luke cite{lu1, lu2, lu3, lu4}, and Joshi and Bissu cite{jb1, jb3}. In this present paper, we introduce some new results for the inequalities of Tricomi functions by using inequalities for the hypergeometric functions under certain additional conditions in section 3. By using a similar technique as inequalities for the Bessel and modified Bessel functions, which may be of interest to themselves, have been discussed briefly for presenting research in section 4.In this subsection, we give certain definitions, lemmas, theorems and formulas to derive our main results. The notations used in cite{jb2, lu1} are followed throughout in this paper. The following lemma brings about various applications in the theory of special functions.In general, we use all the procedures related in cite{jb3} to extend the domain of validity of inequalities for hypergeometric functionsand extend our ideas to get inequalities for these functions. It seems that we have sufficiently elaborated on these points in thiswork and also in our previous study, and further commentary is unnecessary.

Post Author: admin


I'm Eunice!

Would you like to get a custom essay? How about receiving a customized one?

Check it out