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...) of rational functions (which are natural generalizations for meromorphic functions in the non-complex realm) having a zero or a pole at ''P''. ...al ring at a point ''P'' is actually conformed by the germs of holomorphic functions vanishing at ''P''. ...

...}(2,\mathbb{C})</math>-valued one form is locally described by a matrix of functions where <math>a, b, c</math> are allowed to be [[meromorphic]] functions. ...

...er 4</ref> The general problem concerns the question of the existence of a meromorphic function at given values of the exceptional values and associated deficienc ...ongress of Mathematicians|ICM]] in Zurich.<ref>Drasin, David. "Meromorphic functions: progress and problems." In ''Proceedings of the International Congress of ...

...er|1949}} about the [[transcendental number|transcendence]] of values of [[meromorphic function]]s. The theorem implies both the [[Hermite–Lindemann theorem|Herm Fix a [[number field]] {{mvar|K}} and [[meromorphic]] {{math|''f''₁, ..., ''f''_''N''}}, of which at least ...

...totic estimates]] for the coefficients of [[Generating_function|generating functions]].<ref>Melczer 2021, pp. vii and ix.</ref><ref>Pemantle and Wilson 2013, pp ...on#Bivariate_and_multivariate_generating_functions|multivariate generating functions]] started in the 1970s using probabilistic methods.<ref>Melczer 2021, pp. 1 ...

...''Shintani zeta function'' in the variable <math>s</math> is given by (the meromorphic continuation of)<math display="block">\zeta(P;s)=\sum_{x_1,\dots,x_r=1}^{\i == Relation to Witten zeta functions == ...

...ers on the distribution of the values of a meromorphic function, algebraic functions, and coverings. He was one of the devotees of the Hadamard Seminar and he a ...30__5_0 Digitalisat]\</ref> states that for any family <math>F</math> of [[meromorphic function]]s, <math>F</math> is normal if and only if <math>F</math>'s deriv ...

Bloch mainly applied this principle to the theory of [[function (mathematics)|functions]] of a [[complex variable]]. Thus, for example, according to this principl A family <math>\mathcal F</math> of functions [[meromorphic]] on the unit disc <math>\Delta</math> is not normal if and only if there e ...

...reducible highest-weight representations of affine [[Kac–Moody algebra]]s. Meromorphic Jacobi forms appear in the theory of [[Mock modular form]]s. [[Category:Theta functions]] ...

It has a [[meromorphic continuation]] to all complex ''s'', whose only [[Mathematical singularity| ...t2=Ruijsenaars | first2=Simon | title=Shintani&ndash;Barnes zeta and gamma functions | doi=10.1016/j.aim.2003.07.020 | mr=2078341 | year=2004 | journal=[[Advanc ...

{{cite journal |last=Ramachandran |first=Niranjan |year=2015 |title=Zeta functions, Grothendieck groups, and the Witt ring |journal=Bull. Sci. Math. |volume=1 ===Zeta functions of disjoint unions=== ...

...convergence is ''1'' (so ''f'' is holomorphic on the upper half plane and meromorphic at the cusps). ...

...1}}. At the end of this paper he mentioned the existence of multiple gamma functions generalizing it, and studied these further in {{harvtxt|Barnes|1904}}. ...2</math> are closely related to the [[q-gamma function]], and triple gamma functions <math>\Gamma_3</math> are related to the [[elliptic gamma function]]. ...

...,x_n)</math> denote the [[ring (mathematics)|ring]] of [[Smoothness|smooth functions]] in <math>n</math> variables and <math> f</math> a function in the ring. ...ption in terms of polynomials. The <math>F^p</math> part is spanned by the meromorphic forms having poles of order <math>\leq n - p + 1</math> which surjects onto ...

...egative functions. The conjecture has implications in the study of complex functions and is related to Euler's [[Beta function]]. While the conjecture is known == The first statement in terms of logarithmically convex functions == ...

Let ''f'' be a [[meromorphic function]] in the unit disc such that the ''spherical derivative'' satisfie authorlink=Walter Hayman|title=Meromorphic functions|publisher=[[Oxford University Press]]|year=1964}}</ref> ...

...needed to reproduce the usual notion of homogeneity for locally integrable functions, and comes about from the [[integration by substitution|Jacobian change of ...{0}}} are given by various [[power function]]s. In addition to the power functions, homogeneous distributions on '''R''' include the [[Dirac delta function]] ...

more general classes of analytic functions. The main result of the theory is an [[Asymptotic analysis|asymptotic formu ...uthorlink=Georges Valiron|title=Lectures on the general theory of integral functions|year=1949|publisher=Chelsea, reprint of the 1923 ed.|place=NY}}</ref> who n ...

* Rational functions can have Herman rings. According to the result of Shishikura, if a rational ...n]]s can possess Herman rings. Herman rings for transcendental meromorphic functions have been studied by T. Nayak. According to a result of Nayak, if there is ...

...] several important examples of [[automorphic L-function|automorphic ''L''-functions]]. Some authors reserve the term for a special type of integral representa ...and [[Atle Selberg]] independently constructed their [[convolution]] ''L''-functions, now thought of as the Langlands ''L''-function associated to the [[tensor ...