In mathematics, the Clausen function, introduced by Thomas Clausen (1832), is a transcendental, special function of a single variable. It can variously...

Clausen function Complete Fermi–Dirac integral, an alternate form of the polylogarithm. Dilogarithm Incomplete Fermi–Dirac integral Kummer's function...

{z^{k}}{k^{s}}}} which coincides with the Riemann zeta function when z = 1. The Clausen function Cls(θ) can be chosen as the real or imaginary part of...

discovered the Clausen function. In 1842, Clausen was hired by the staff of the Tartu Observatory, becoming its director in 1866–1872. Works by Clausen include...

{\displaystyle \psi ^{(n)}(\alpha )=(-1)^{n+1}n!\Phi (1,n+1,\alpha )} The Clausen function: Cl 2 ( z ) = i e − i z 2 Φ ( e − i z , 2 , 1 ) − i e i z 2 Φ ( e i...

A similar result holds for the trigamma function but the circular functions are replaced by Clausen's function. Namely, ψ 1 ( p q ) = π 2 2 sin 2 ⁡ ( π...

then expressing those Clausen functions in terms of the Barnes G-function, the following expression is obtained (see Clausen function for more): G = 4 π...

has since been replaced by ԓ. El is sometimes used to represent the Clausen function, and if not, the capital greek letter Lambda is. Λ λ : Greek letter...

} The function D(z) is sometimes called the Bloch-Wigner function. Lobachevsky's function and Clausen's function are closely related functions. William...

Clausen is a Danish patronymic surname, literally meaning child of Claus, Claus being a German form of the Greek Νικόλαος, Nikolaos, (cf. Nicholas), used...

log-tangent integral on the right-hand side can be evaluated in terms of the Clausen function (of order 2), as is shown below: 2 π log ⁡ ( G ( 1 − z ) G ( 1 + z...

09653\ 62502\ 12025\dots } It can be given as in a closed form with the Clausen function Cl 2 ⁡ ( φ ) {\displaystyle \operatorname {Cl} _{2}\left(\varphi \right)}...

Lobachevsky Prize, including the Lobachevsky Medal Lobachevsky function, also called the Clausen function "Lobachevsky" (song), a humorous song by Tom Lehrer Hyperbolic...

polylogarithm with pure imaginary μ may be expressed in terms of the Clausen functions Cis(θ) and Sis(θ), and vice versa (Lewin 1958, Ch. VII § 1.4; Abramowitz...

a complex number that can be expressed as an integral of an algebraic function over an algebraic domain. The periods are a class of numbers which includes...

Wiktionary, the free dictionary. CL2 may refer to: Chlorine gas, Cl2 the Clausen function of order 2, Cl2 the Clifford algebra on C 2 {\displaystyle \mathbb...

Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, ISBN 978-0-521-62321-6, MR 1688958 Clausen, Thomas...

In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied...

This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks...

Dyggve-Melchior-Clausen (DMC) Syndrome is a rare autosomal recessive disorder that stunts skeletal and intellectual development. Individuals with this...

Tim Clausen (born 12 March 1969) is a structural biologist and a senior scientist at the Research Institute of Molecular Pathology (IMP) in Vienna, Austria...

complex numbers leads to the following paradox, discovered in 1827 by Clausen: For any integer n, we have: e 1 + 2 π i n = e 1 e 2 π i n = e ⋅ 1 = e...

an ideal tetrahedron can be expressed in terms of the Clausen function or Lobachevsky function of its dihedral angles, and the volume of an arbitrary...

coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over...

(4): 340–341. doi:10.1634/theoncologist.4-4-340. PMID 10476546. Wu P, Clausen MH, Nielsen TE (December 2015). "Allosteric small-molecule kinase inhibitors"...

{6}}.\end{cases}}} The von Staudt–Clausen theorem was given by Karl Georg Christian von Staudt and Thomas Clausen independently in 1840. The theorem...

1892 1 February 1944 Commentator, news analyst Watching the World George Clausen United Kingdom 18 April 1852 22 November 1944 Artist J. Storer Clouston...

157; Knuth attributes the transformation to this form to an 1828 work of Clausen. Erdős, P. (1948), "On arithmetical properties of Lambert series" (PDF)...

Čaval, Tomislav; Zhu, Jing; Tian, Weihua; Remmelzwaal, Sanne; Yang, Zhang; Clausen, Henrik; Heck, Albert J. R. (2019-01-01). "Targeted Analysis of Lysosomal...

minister's son. The police eventually conclude that Aaron's friend Rowan Clausen committed both murders, having always been the instigator for friend activities...