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...

a_{n}} is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory...

(number theory) Dirichlet series (analytic number theory) Dirichlet series inversion General Dirichlet series Dirichlet space Dirichlet stability criterion...

Like the zeta function, Dirichlet series in general play an important role in analytic number theory. Generally a Dirichlet series converges if the real...

series expansion on an annulus centered at the singularity. A general Dirichlet series is a series of the form ∑ n = 1 ∞ a n e − λ n s . {\textstyle \sum _{n=1}^{\infty...

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

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...

are several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral...

In mathematics, the Dirichlet boundary condition is imposed on an ordinary or partial differential equation, such that the values that the solution takes...

{\textstyle \arctan 1={\tfrac {1}{4}}\pi .} It also is the Dirichlet L-series of the non-principal Dirichlet character of modulus 4 evaluated at s = 1 , {\displaystyle...

Z → C {\displaystyle \chi :\mathbb {Z} \rightarrow \mathbb {C} } is a Dirichlet character of modulus m {\displaystyle m} (where m {\displaystyle m} is...

Fourier series converges to the average of the left and right limits (but see Gibbs phenomenon). The Dirichlet–Dini Criterion (see Dirichlet conditions...

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...

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...

Bell series, and Dirichlet series. Every sequence in principle has a generating function of each type (except that Lambert and Dirichlet series require...

Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons...

In analytic number theory, a Dirichlet series, or Dirichlet generating function (DGF), of a sequence is a common way of understanding and summing arithmetic...

naturally in the study of Dirichlet series such as the Riemann zeta function. It describes the multiplication of two Dirichlet series in terms of their coefficients:...

the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any complex number having...

generalisations of the Riemann zeta function and the L-series for a Dirichlet character are constructed, and their general properties, in most cases still out of reach...

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...

determined by a combination of inflation rates and interest rates. In general, a geometric series is written as a + a r + a r 2 + a r 3 + . . . {\displaystyle...

In the 14th century, the earliest examples of specific Taylor series (but not the general method) were given by Indian mathematician Madhava of Sangamagrama...

coefficients of the Dirichlet series representation of the Dedekind zeta function. The n-th coefficient of the Dirichlet series is essentially the number...

They occur, for example, in the functional equations of Dirichlet L-functions, where for a Dirichlet character χ the equation relating L(s, χ) and L(1 − s...

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

begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions...

can be proven using the Dirichlet hyperbola method, and was first established by Dirichlet in 1849.: 37–38, 69  The Dirichlet divisor problem, precisely...

some convergent alternating series may fail the first part of the test. For a generalization, see Dirichlet's test. A series of the form ∑ n = 0 ∞ ( − 1...

placing hierarchical Dirichlet process priors over the HMM transition matrix. Step detection Keogh, Eamonn, et al. "Segmenting time series: A survey and novel...