Displaying similar documents to “On some questions concerning lacunary power series of two variables”

Sums of an entire function in certain weighted L-spaces.

Bruno Brive (2003)

Publicacions Matemàtiques

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We consider the functional equation f(z+σ) - f(z) = g(z) where σ is a complex number, f and g are entire functions of a complex variable z, with growth conditions. We prove the existence of certain types of solutions of this equation by an a priori estimate method in certain weighted L-spaces.

On the power-series expansion of a rational function

D. V. Lee (1992)

Acta Arithmetica

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Introduction. The problem of determining the formula for P S ( n ) , the number of partitions of an integer into elements of a finite set S, that is, the number of solutions in non-negative integers, h s ₁ , . . . , h s k , of the equation hs₁ s₁ + ... + hsk sk = n, was solved in the nineteenth century (see Sylvester [4] and Glaisher [3] for detailed accounts). The solution is the coefficient of x ⁿ i n [(1-xs₁)... (1-xsk)]-1, expressions for which they derived. Wright [5] indicated a simpler method by which to find part...