Lerch zeta function information

mathematics, the Lerch zeta function, sometimes called the Hurwitz–Lerch zeta function, is a special function that generalizes the Hurwitz zeta function and the...

function Ihara zeta function of a graph L-function, a "twisted" zeta function Lefschetz zeta function of a morphism Lerch zeta function, a generalization...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

In mathematics, the Hurwitz zeta function is one of the many zeta functions. It is formally defined for complex variables s with Re(s) > 1 and a ≠ 0,...

universality of zeta functions is the remarkable ability of the Riemann zeta function and other similar functions (such as the Dirichlet L-functions) to approximate...

football coach Gustov C. Lerch House Lerch Bates Lerch zeta function Lorch (disambiguation) This page lists people with the surname Lerch. If an internal link...

1,-x\right)}{\Gamma (-x)}}} where Φ {\displaystyle \Phi } is the Lerch zeta function. We also have the Luschny factorial: Γ ( x + 1 ) ( 1 − sin ⁡ ( π...

gamma function satisfies the following formula due to Lerch: log ⁡ Γ ( z ) = ζ H ′ ( 0 , z ) − ζ ′ ( 0 ) , {\displaystyle \log \Gamma (z)=\zeta _{H}'(0...

Sciences for his number-theoretic work. The Lerch zeta function is named after him, as is the Appell–Lerch sum. His doctoral students include Michel Plancherel...

Dirichlet beta function Dirichlet L-function Hurwitz zeta function Legendre chi function Lerch transcendent Polylogarithm and related functions: Incomplete...

t\\&=(-1)^{m+1}m!\zeta (m+1,z)\end{aligned}}} where ζ ( s , q ) {\displaystyle \zeta (s,q)} is the Hurwitz zeta function. This expresses the polygamma function as the...

relationships given in those articles. The Legendre chi function is a special case of the Lerch transcendent, and is given by χ ν ( z ) = 2 − ν z Φ ( z...

\left(s,{1 \over 4}\right)-\zeta \left(s,{3 \over 4}\right)\right).} Another equivalent definition, in terms of the Lerch transcendent, is: β ( s ) =...

transformations defined above is related to more Hurwitz-zeta-like, or Lerch-transcendent-like, generating functions. Specifically, if we define the even more general...

functions are special cases of the Lerch transcendent. Polylogarithms should not be confused with polylogarithmic functions, nor with the offset logarithmic...

1007/s11139-007-9102-0. S2CID 14910435. (Reviews relationship to the Hurwitz zeta function and Lerch transcendent.) Hugh L. Montgomery; Robert C. Vaughan (2007). Multiplicative...

numbers List of physical constants Particular values of the Riemann zeta function Physical constant Both i and −i are roots of this equation, though neither...

(2019). "A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function". Mathematics. 7 (1148): 1148. doi:10.3390/math7121148...

(2000). "The joint universality and the functional independence for Lerch zeta-functions". Nagoya Mathematical Journal. 157 (2000): 211–227. doi:10.1017/S002776300000725X...

group of the ring of integers of a number field to the field's Dedekind zeta function. Bombieri–Lang conjectures on densities of rational points of algebraic...

PMC 2199947. PMID 7642713. Schnekenburger J, Mayerle J, Simon P, Domschke W, Lerch MM (1999). "Protein tyrosine dephosphorylation and the maintenance of cell...