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...than 1. By [[analytic continuation]], this function can be extended to a [[meromorphic function]] on the whole [[complex plane]], and is then called a '''Dirichle These functions are named after [[Peter Gustav Lejeune Dirichlet]] who introduced them in { ...

...> the elliptic modulus, in which case the solutions extend to meromorphic functions defined on the whole complex plane. For other values of ''B'' the solutions where <math> k </math> is the elliptic modulus of the Jacobian elliptic functions and <math> \kappa</math> and <math> \Omega</math> are constants. For <math> ...

...rgent]] for the given values of ''s'' and ''q'' and can be extended to a [[meromorphic function]] defined for all ''s''&ne;1. The [[Riemann zeta function]] is &ze ...Hurwitz zeta function can be extended by [[analytic continuation]] to a [[meromorphic function]] defined for all complex numbers <math>s</math> with <math>s \neq ...

...are used more often in practical problems than the [[Weierstrass elliptic functions]] as they do not require notions of complex analysis to be defined and/or u ...denoted by pq(u,m), where p and q are any of the letters c, s, n, and d. (Functions of the form pp(u,m) are trivially set to unity for notational completeness. ...

...ther". There are several common standard forms of confluent hypergeometric functions: ...ns are essentially the same, and differ from each other only by elementary functions and change of variables. ...

{{short description|Special functions of several complex variables}} {{for|other θ functions|Theta function (disambiguation)}} ...

...ny particular [[special functions]] as special cases, such as [[elementary functions]], [[Bessel function]]s, and the [[orthogonal polynomials|classical orthogo ...irst3=O. I.|last3=Marichev|title=Integrals & Series Volume 3: More Special Functions|publisher=Gordon and Breach|year=1990|pages=439}}</ref> ...

...he Euler definition to a [[complex number|complex]] variable, proved its [[meromorphic]] continuation and [[functional equation]], and established a relation betw ...et L-function|Dirichlet {{mvar|L}}-functions]] and [[L-function|{{mvar|L}}-functions]], are known. ...

...defined as the [[analytic continuation]] of this integral function to a [[meromorphic function]] that is [[holomorphic function|holomorphic]] in the whole comple ...popular and useful. It is a component in various probability-distribution functions, and as such it is applicable in the fields of [[probability]] and [[statis ...

...upper''' and '''lower incomplete gamma functions''' are types of [[special functions]] which arise as solutions to various mathematical problems such as certain ...]</ref> Complex analysis shows how properties of the real incomplete gamma functions extend to their holomorphic counterparts. ...