Related papers: A remark on the matrix Airy function
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.
We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help of residue calculus we explicitly show how the integral…
We prove a decay estimate for an operator that arises in two-dimensional scattering problem.
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
The Airy function Ai(z) and its derivative Ai'(z) occur in a large number of applications in Chemistry and Physics. As a result, there is a continuing interest in the properties of these functions. Recently, there has been interest in…
We construct rational all-pass matrix functions with real-valued coefficients for mirroring pairs of complex-conjugated determinantal roots of a rational matrix. This problem appears, for example, when proving the spectral factorization…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
In this note we present a version of Hardy's inequality on a measure space $(X,\mu)$ endowed with a measurable function $N\colon X\to \mathbb R$ which replaces the absolute value on $\mathbb R$ or $\mathbb R^n$, and, more generally, the…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
In the paper, the authors find some integral representations and discover some properties of Lah numbers.
We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that…
We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space $\mathcal H^1$, the other one in its dual, belongs to a Hardy type space. Conversely, every holomorphic function in this space…
A general approach for evaluating the nonfactorizable contributions to the hadronic matrix elements is described in terms of the higher twist wave functions of the mesons. An example is illustrated for the $B^{0} \to \pi^{+}\pi^{-}$ decays.
Using a pointwise version of Fej\'{e}r's theorem about Fourier series, we obtain two formulae related to the series representations of positive integral powers of $\pi$. We also check the correctness of our formulae by the applications of…
A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…