Function (biology)

Logarithmic derivative

Pure mathematics

Biology

Gravitational singularity

Bessel function

Hankel transform

Evolutionary biology

Mathematics

Asymptotic expansion

Mathematical analysis

Combinatorics

Logarithm

Computers & Mathematics with Applications

Asymptotic expansions as λ → +∞ are obtained for the Hankel transform ΩV(λ)=∫0∞JV(λt)f(t)dtwhereJv(t) is the Bessel function of the first kind and v is a fixed complex number. The function \tf(t) is allowed to have an asymptotic expansion near the origin of the form f(t)∼∑n=0∞Cntαn(–lnt)βnHere, Re αn ↑ +∞ and βn is an arbitrary complex number.

Asymptotic expansions of Hankel transforms of functions with logarithmic singularities