In mathematical analysis, Darboux's formula is a formula introduced by Gaston Darboux (1876) for summing infinite series by using integrals or evaluating...

Maclaurin used it to calculate integrals. It was later generalized to Darboux's formula. If m and n are natural numbers and f(x) is a real or complex valued...

invariants Darboux or Goursat problem Darboux transformation Darboux vector Darboux's problem Darboux's theorem in symplectic geometry Darboux's theorem...

In mathematics, the Christoffel–Darboux formula or Christoffel–Darboux theorem is an identity for a sequence of orthogonal polynomials, introduced by Elwin...

polynomials as special cases. These are frequently given by the Rodrigues' formula. The field of orthogonal polynomials developed in the late 19th century...

he also introduced the Christoffel–Darboux formula for Legendre polynomials (he later also published the formula for general orthogonal polynomials)...

equation, Christoffel symbols, Schwarz–Christoffel mapping, Christoffel–Darboux formula Louis Christoffel (1886–?), Belgian wrestler Martin Christoffel (1922–2001)...

motion. Roughly speaking, the Frenet–Serret formulas express the Darboux derivative of the TNB frame. If the Darboux derivatives of two frames are equal, then...

In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame...

T(n)={\frac {\operatorname {He} _{n}(i)}{i^{n}}}.} The Christoffel–Darboux formula for Hermite polynomials reads ∑ k = 0 n H k ( x ) H k ( y ) k ! 2 k...

P_{n}^{(\alpha ,\beta )}} for large n {\displaystyle n} is given by the Darboux formula: VIII.2  P n ( α , β ) ( cos ⁡ θ ) = n − 1 2 k ( θ ) cos ⁡ ( N θ +...

symmetric kernel polynomial has the representations (Christoffel–Darboux formula)[citation needed] K n ( α ) ( x , y ) := 1 Γ ( α + 1 ) ∑ i = 0 n L...

these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many...

three term recurrence or the Christoffel-Darboux formula hold. There exist however other recursion formulas for certain types of measures. There exist...

x_{i}} ) is contained between the lower and upper Darboux sums. This forms the basis of the Darboux integral, which is ultimately equivalent to the Riemann...

In mathematics, the Darboux transformation, named after Gaston Darboux (1842–1917), is a method of generating a new equation and its solution from the...

The Darboux integral, which is defined by Darboux sums (restricted Riemann sums) yet is equivalent to the Riemann integral. A function is Darboux-integrable...

centers of force. Special cases of these generalized problems include Darboux's problem and Velde's problem. Euler's three-body problem is to describe...

circle method. Walter Hayman's 1956 paper "A Generalisation of Stirling's Formula" is considered one of the earliest examples of the saddle-point method...

mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle...

supremum on that subinterval.) The Darboux integral, which is similar to the Riemann integral but based on Darboux sums, is equivalent to the Riemann...

symplectic structure constant, by Darboux's theorem; and, using the associated Poisson bivector, one may consider the above formula. For it to work globally,...

polynomials, which are also called the Mehler–Heine formula. The formula complements the Darboux formulae which describe the asymptotics in the interior...

is the standard argument for the modern proof of Darboux's theorem, as well as for the proof of Darboux-Weinstein theorem and other normal form results...

bodies, presented on December 21, 1807 to the National Institute]. In Darboux, Gaston (ed.). Oeuvres de Fourier [The Works of Fourier] (in French). Vol...

theorem – gives the Taylor series of the inverse of an analytic function Darboux's theorem – states that all functions that result from the differentiation...

{E} [f(X)]=\int _{-\infty }^{\infty }f(x)g'(x)\,\mathrm {d} x.} But this formula does not work if X does not have a probability density function with respect...

less intuitive than the definition in terms of the osculating circle, but formulas for computing the curvature are easier to deduce. Therefore, and also because...

frame (aircraft principal axes) when described by the pilot. Darboux frame Frenet–Serret formulas Turtle graphics Yaw, pitch, and roll Chern 1985 D. J. Struik...

Mehler, student of Dirichlet (Ferdinand): Mehler's formula, Mehler–Fock formula, Mehler–Heine formula, Mehler functions Meijer G-function Josef Meixner:...