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In analysis, a lacunary function, also known as a lacunary series, is an analytic function that cannot be analytically continued anywhere outside the...

In complex analysis, a subfield of mathematics, a lacunary value or gap of a complex-valued function defined on a subset of the complex plane is a complex...

band Lacunary function, an analytic function in mathematics Lacunarity, a mathematical measure of the extent that a pattern contains gaps Lacunary polynomial...

… , X n ) = P lacunary ( X 1 , … , X n ) + X 1 ⋯ X n ⋅ Q ( X 1 , … , X n ) . {\displaystyle P(X_{1},\ldots ,X_{n})=P_{\text{lacunary}}(X_{1},\ldots ...

of f {\textstyle f} are missing a single point, this point is called a lacunary value of the function. Great Picard's Theorem: If an analytic function...

condition (*). An example found by Marcus and Shepp : 387  is a random lacunary Fourier series X t = ∑ n = 1 ∞ c n ( ξ n cos ⁡ λ n t + η n sin ⁡ λ n t...

In mathematics, a sparse polynomial (also lacunary polynomial or fewnomial) is a polynomial that has far fewer terms than its degree and number of variables...

ions, giving a defect structure called a lacunary structure. An example of a compound with a Dawson lacunary structure is As2W15O56. In 2014, vanadate...

essential way. For integers c ≥ 2 {\displaystyle c\geq 2} , we define the lacunary series of order c by the power series expansion L c ( z ) := ∑ n ≥ 1 z...

Archived (PDF) from the original on 2017-10-31. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6):...

Mo3O13 units, which lowers the symmetry of the overall structure. The term lacunary is applied to ions which have a fragment missing, sometimes called defect...

tablets. It is the first known mineral to contain a heteropolyanion, a lacunary defect derivative of the Keggin anion. The chemical formula of ophirite...

exception. When an exception exists, it is called a lacunary value of the function. The possibility of a lacunary value is illustrated by the exponential function...

{\displaystyle \mathbb {C} } , or C {\displaystyle \mathbb {C} } excluding one lacunary value. These definitions for the exponential and trigonometric functions...

showed that every lacunary sequence of integers is in fact a "bad universal sequence" in L 1 {\displaystyle L_{1}} . Thus lacunary sequences are ‘canonical’...

unity was originally a conjecture made by Ostrowski in the context of lacunary series. Chebotarev was the first to prove it, in the 1930s. This proof...

the investigations of lacunary polynomials over finite fields, which he eventually published in a book. This work on lacunary polynomials has had a big...

doi:10.3138/md.39.1.156. S2CID 191356034. Wittig, Monique (15 July 1996). "Lacunary films". New Statesman. 102. Progressive Media International. Wittig, Monique...

analysis and harmonic analysis, with an emphasis on Dirichlet series, lacunary series, and entire functions. Rather than a Bourbakist, he is perhaps more...

compositions at various pH values are as follows: The species [PW11O39]7− is a lacunary, or defective Keggin ion. The [P2W18O62]6− has a Dawson structure. At pH...