Related papers: Lagrange Inversion Formula by Induction

We show how the asymptotic expansion for the gamma function $\Gamma(x)$, similar to that obtained by Boyd [Proc. Roy. Soc. London A447 (1994) 609--630], can be obtained by using a form of Lagrange's inversion theorem with a remainder. A…

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

The objective of this paper is to present an approximation formula for the Katugampola fractional integral, that allows us to solve fractional problems with dependence on this type of fractional operator. The formula only depends on…

A vector variational principle is proved.

There is a simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature. An equation for the gauge…

The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…

Khabibullin's conjecture deals with two linear integral inequalities for some non-negative continuous function $q(t)$. The integral in the first of these two inequalities converts $q(t)$ into another function of one variable $g(t)$. This…

Motivated by stereology, based on Novikov's inversion formula, we prove a Plancherel-type formula for the attenuated Radon transform.

We present a pedagogical description of the inversion of Gamow's tunnelling formula and we compare it with the corresponding classical problem. We also discuss the issue of uniqueness in the solution and the result is compared with that…

We provide a new characterization of the logarithmic Sobolev inequality.

Formulae relating one and the same force in two inertial frames of reference are derived directly from the Lorentz transformation of space and time coordinates and relativistic equation for the dynamic law of motion in three dimensions. We…

We invert the second order, single field, general slow-roll formula for the power spectrum, to obtain a second order formula for inflationary parameters in terms of the primordial power spectrum.

We give a relatively short and self contained proof of Ratner's theorem in the special case of SL(2,R)-invariant measures.

The article provides the formula for the calculation the falling time of inverted pendulum. The result is expressed in terms of elliptic integrals of first kind. The asymptotic formula for small initial inclination value is also provided.

In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series. In addition some of…

We formulate the Lagrange-D'Alembert principle as a pure mathematical theory that meets modern standards of rigor. While we note several new aspects of the principle, the article is primarily methodological.

In this paper, we develop an elementary proof of the change of variables in multiple integrals. Our proof is based on an induction argument. Assuming the formula for (m-1)-integrals, we define the integral over hypersurface in Rm, establish…

Landau damping is calculated using real variables, clarifying the physical mechanism.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

This article present a new, direct and simple formula for constructing Mignotte sequences.