Yutian Li

Integral and series representations of the dirac delta function

Mathematical justifications are given for several integral and series representations of the Dirac delta function which appear in the physics literature. These include integrals of products of Airy functions, and of Coulomb wave functions; they also include series of products of Laguerre polynomials and of spherical harmonics. The methods used are essentially based on the asymptotic behavior of these special functions.

Full asymptotic expansions of the Landau constants via a difference equation approach

Abstract We derive full asymptotic expansions for the Landau constants G n as n → ∞ . Some of the expansions are not new, yet all the coefficients of the expansions are given iteratively in an explicit manner, and are more efficiently evaluated as compared with the known results. We obtain the asymptotic formulas, old and new, by applying the theory of Wong and Li for second-order linear difference equations. In deriving the expansions, we have also confirmed a conjecture made by Nemes and Nemes.

Asymptotics of Landau Constants with Optimal Error Bounds

We study the asymptotic expansion for the Landau constants

Option prices under stochastic volatility

G_n

Valuation of American options under the CGMY model

Gn,

A fundamental solution for a nonelliptic partial differential operator, II

\begin{aligned} \pi G_n\sim \ln N + \gamma +4\ln 2 + \sum _{s=1}^\infty \frac{\beta _{2s}}{ N^{2s}},\quad n\rightarrow \infty , \end{aligned}