Search results

function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis...

define the sum of the divergent series by the limit above. A series of this type is known as a generalized Dirichlet series; in applications to physics,...

In the field of mathematical analysis, a general Dirichlet series is an infinite series that takes the form of ∑ n = 1 ∞ a n e − λ n s , {\displaystyle...

of the heat kernel. In mathematics, such a sum is known as a generalized Dirichlet series; its use for averaging is known as an Abelian mean. It is closely...

average Dirichlet distribution (probability theory) Dirichlet-multinomial distribution Dirichlet negative multinomial distribution Generalized Dirichlet distribution...

Johann Peter Gustav Lejeune Dirichlet (German: [ləˈʒœn diʁiˈkleː]; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved...

\setminus \{1\}} with a simple pole at 1. This series can be directly generalized to general Dirichlet series. A series of functions in which the terms are trigonometric...

In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there...

squares. Generalized Dirichlet distribution Grouped Dirichlet distribution Inverted Dirichlet distribution Latent Dirichlet allocation Dirichlet process...

prove, is the Taylor series of the desired solution. The Taylor series may also be generalized to functions of more than one variable with T ( x 1 , … , x...

In mathematics, a Dirichlet L-series is a function of the form L ( s , χ ) = ∑ n = 1 ∞ χ ( n ) n s . {\displaystyle L(s,\chi )=\sum _{n=1}^{\infty }{\frac...

instance of the Dirichlet theorem for Fourier series. This example leads to a solution of the Basel problem. A proof that a Fourier series is a valid representation...

functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series; definitions and examples are given below. Every sequence...

at x, then the Fourier series converges to the average of the left and right limits (but see Gibbs phenomenon). The Dirichlet–Dini Criterion states that:...

mathematics, Dirichlet's test is a method of testing for the convergence of a series. It is named after its author Peter Gustav Lejeune Dirichlet, and was...

one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an...

{2}{k}}f^{(2-k)}(x)g^{(k)}(x)}=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x).} The formula can be generalized to the product of m differentiable functions f1,...,fm. ( f 1 f 2 ⋯ f...

commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 treatment of the principle by Peter Gustav Lejeune Dirichlet under the...

methods of summability, then the Dirichlet series for η defines a function on the whole complex plane — the Dirichlet eta function — and moreover, this...

In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called...