We classify them in several categories depending on the asymptotic principles from which they are obtained: classical methods based on Watson's lemma, summability methods, distributional methods, Mellin transform
techniques, integration by parts, and so on.
of the product Y, we take double Mellin transform
Following Hadamard's precept, these problems are tackled by complex analysis methods such as generating functions, Mellin transform
, Fourier series, saddle point method, analytic poissonization and depoissonization, and singularity analysis.
This will be achieved essentially by using the Mellin transform
He also develops Mellin transform
techniques used to evaluate said integrals analytically and express the results either as infinite series or as sums of generalized hypergeometric functions.
However, we could not take the multiple Mellin transform
to define multiple p-adic L-function which interpolates multiple Bernoulli numbers.
Keywords: Fragmentation models, fixed point, contraction method, Mellin transform
Using the well-known properties of the Mellin transform
(see (FGD95) and (Szp01)), it follows that
The proof of Proposition 2 consists of three steps: (i) the Poisson expectation is first expressed in integral form (Equation (9)); (ii) the integrand is next analysed by means of the Mellin transform
(Lemma 1); (iii) the outcome of the local Mellin analysis is finally used to estimate the Poisson expectation.
Keywords: Random walk in the plane, exit time, number of paths, Tunstall's code, Khodak code, Mellin transform
, Tauberian theorems.
It is also shown from an analysis of the moving poles of the Mellin transform
of the poissonized moment generating function that the imbalance factor (under appropriate centering and scaling) follows a Gaussian limit law.
Keywords: Motzkin paths, singularity analysis, Mellin transform
, bootstrapping, unary-binary trees, Gumbel distribution