Related papers: On the Complex Conjugate Series for Pi
A translation of Kummer`s paper On certain definite integrals and infinite series
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
We propose a class of Pad\'e interpolation problems whose solutions are expressible in terms of determinants of hypergeometric series.
By means of the extended Gould-Hsu inverse series relations, we find that the dual relation of Dougall's summation theorem for the well--poised $_7F_6$-series can be utilized to construct numerous interesting Ramanujan--like infinite series…
A general solution to the Complex Monge-Amp\`ere equation in a space of arbitrary dimensions is constructed.
Let W be a Coxeter group. We show that a certain power series involving a sum over all involutions in W can be expressed in terms of the Poincare series of W. (The case where W is finite is already known,)
We prove that in normal rings the tight closure of an ideal can be computed as the sum of the ideal and a piece of the tight closure, called the special tight closure.
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…
In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…
We propose the definition of a Manifold with a complex Lie structure at infinity. The important class of ACH manifolds enters into this class.
In this paper we show how to apply various techniques and theorems (including Pincherle's theorem, an extension of Euler's formula equating infinite series and continued fractions, an extension of the corresponding transformation that…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by…
We present here two classes of infinite series and the associated continued fractions involving $\pi$ and Catalan's constant $G$ based on the work of Euler and Ramanujan. A few sundry continued fractions are also given.
The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…
A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters
It is shown that, given a representation of a quiver over a finite field, one can check in polynomial time whether it is absolutely indecomposable.
We consider some Diophantine problems of mixed modular-multiplicative type associated with the Zilber-Pink conjecture. In particular, we prove a finiteness statement for the number of multiplicative relations between singular moduli…