Related papers: Lagrange Inversion Formula by Induction
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
A method for constructing Lagrangians for the Lie transformation groups is explained. As examples, the Lagrangians for real plane rotations and affine transformations of the real line are constructed.
We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal…
We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier…
We give a simple derivation of the Plancherel measure for Lebedev-Whittaker transforms on GL(n).
In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.
In this short note I restate and simplify the proof of the impossibility of probabilistic induction from Popper (1992). Other proofs are possible (cf. Popper (1985)).
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…
In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal…
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
We describe a method to compute Hurwitz-Hodge integrals.
Using explicit weakenings, we can define alpha-conversion by simple equations without any mention of free variables.
For absolutely convergent series we state explicitly a one-sided summation estimate that can be viewed as the discrete analogue of the change of variable formula on the half line. This estimate is implicit in Pascal Lef\`evre's recent…
A fast Fourier transform method for computing the weight enumerator polynomial and trigonometric degree of lattice rules is introduced.
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.
The proof of the theorem concerning to the inverse cyclotomic Discrete Fourier Transform algorithm over finite field is provided.