Inequalities for the modified Bessel function of first kind and its consequences

Abstract: Study on asymptotics of modified Bessel functions dates back to 18th century. In this talk, we will describe how from the study of asymptotics of modified Bessel function of first kind of non-negative order, one can comes up with a host of inequalities that finally leads to answer combinatorial properties, for example log-concavity, higher order Tur\acute{a}n inequality of certain arithmetic sequences arising from Fourier coefficients of modular forms. In addition to that, we will discuss briefly on a result of Bringmann et al. and analyze with the work addressed above.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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