## 528 Citations

### Mellin Transforms : Harmonic Sums

- Mathematics, Computer Science
- 2008

The Mellin transform is useful to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the average-case analysis of algorithms.

### Asymptotics of some generalized Mathieu series

- Mathematics
- 2019

We establish asymptotic estimates of Mathieu-type series defined by sequences with power-logarithmic or factorial behavior. By taking the Mellin transform, the problem is mapped to the singular…

### Mellin Transforms and Asymptotics: Finite Differences and Rice's Integrals

- MathematicsTheor. Comput. Sci.
- 1995

### Asymptotic Analysis of Regular Sequences

- MathematicsAlgorithmica
- 2019

It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations multiplied by a scaling factor.

### Asymptotics and statistics on Fishburn matrices and their generalizations

- MathematicsJ. Comb. Theory, Ser. A
- 2021

### Asymptotic behaviour of some infinite products involvingprime numbers

- Mathematics
- 1996

The asymptotic behaviour of some entire functions defined via infinite products is investigated as the parameter z tends to infinity in the sector | arg z| < π. These functions arise in the…

### Asymptotic Behaviour of a Non-commutative Rational Series with a Nonnegative Linear Representation

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2007

A Fourier representation of a first-order summation function obtained by interpreting this rational series as a non-classical rational sequence via the octal numeration system is derived.

### Approximate Counting via the Poisson-Laplace-Mellin Method

- Computer Science, Mathematics
- 2012

This paper proposes a new analysis via the Poisson-Laplace-Mellin approach, a method devised for analyzing shape parameters of digital search trees in a recent paper of Hwang et al, that yields a different and more compact expression for the periodic function from the asymptotic expansion of the variance.

## References

SHOWING 1-10 OF 100 REFERENCES

### Mellin Transforms and Asymptotics: Finite Differences and Rice's Integrals

- MathematicsTheor. Comput. Sci.
- 1995

### Singularity Analysis of Generating Functions

- MathematicsSIAM J. Discret. Math.
- 1990

This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic…

### Introduction to the Theory of Fourier Integrals

- MathematicsNature
- 1938

SINCE the publication of Prof. Zygmund's “Trigonometric Series” in 1935, there has been considerable demand for another book dealing with trigonometric integrals. Prof. Titchmarsh's book meets this…

### Exact Asymptotics of Divide-and-Conquer Recurrences

- Computer ScienceICALP
- 1993

This work shows that periodicity phenomena, often of a fractal nature, are ubiquitous in the performances of top-down recursive mergesort algorithms.

### Automatic Average-Case Analysis of Algorithm

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1991

### The theory of partitions

- Mathematics
- 1976

1. The elementary theory of partitions 2. Infinite series generating functions 3. Restricted partitions and permutations 4. Compositions and Simon Newcomb's problem 5. The Hardy-Ramanujan-Rademacher…

### The Theory of the Riemann Zeta-Function

- Mathematics
- 1987

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects…

### Tables of Mellin Transforms

- Mathematics
- 1974

I. Mellin Transforms.- Some Applications of the Mellin Transform Analysis.- 1.1 General Formulas.- 1.2 Algebraic Functions and Powers of Arbitrary Order.- 1.3 Exponential Functions.- 1.4 Logarithmic…

### The Laplace Transform

- MathematicsNature
- 1943

THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulæThe Laplace TransformBy David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton…