arXiv subjects

Nathalie Liezel R. Rojas

Publications and source records attributed to Nathalie Liezel R. Rojas.

2 recordsLinked to original sources

arXiv2025

Asymptotic evaluation of the Sinc transform of entire exponential type function resulting to exact polynomial asymptotic behavior

We consider the asymptotic evaluation of the integral transform $\int_0^\infty f(x) \, \sin^n(λx)/x^n \,\text{d} x$ of an exponential type function $f(x)$ of type $τ>0$, for large values of the parameter $λ$, where $n$ is a positive integer. We refer to this integral as the Sinc transform. Under the condition that $f(x)$ is even with respect to $x$, we derive a terminating asymptotic expansion of the Sinc transform which behave as a polynomial in positive powers of $λ$ as $λ$ grows large provided that the conditions $λ> τ/2$ for even $n$ and $λ>τ$ for odd n are satisfied.

math.CA↗

arXiv2024

Terminating Poincare asymptotic expansion of the Hankel transform of entire exponential type functions

We perform an asymptotic evaluation of the Hankel transform, $\int_0^{\infty}J_ν(λx) f(x)\mathrm{d}x$, for arbitrarily large $λ$ of an entire exponential type function, $f(x)$, of type $τ$ by shifting the contour of integration in the complex plane. Under the situation that $J_ν(λx)f(x)$ has an odd parity with respect to $x$ and the condition that the asymptotic parameter $λ$ is greater than the type $τ$, we obtain an exactly terminating Poincar{é} expansion without any trailing subdominant exponential terms. That is the Hankel transform evaluates exactly into a polynomial in inverse $λ$ as $λ$ approaches infinity.

math.CV↗