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Formula di Itô
La formula di Itô è lo strumento più importante del calcolo differenziale stocastico. In questo capitolo ne presentiamo diverse versioni che...
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The Trace Formula
This chapter is devoted to the trace formula connecting the spectrum of a finite compact metric graph with the set of closed paths on it. In other...
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Stirling’s Formula
We obtain Stirling’s Formula (due to de Moivre) which estimates \(n!\)...
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Trace Formula and Inverse Problems
Our aim in this section is to establish an explicit formula allowing one to calculate the Euler characteristic of the metric graph directly from the...
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Postlude: Stirling’s Formula Again
We obtain Stirling’s Formula (due to Stirling) which estimates \(n!\)...
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Exact formula for cubic partitions
We obtain an exact formula for the cubic partition function and prove a conjecture by Banerjee, Paule, Radu and Zeng.
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A New Regularized Siegel-Weil Type Formula. Part I
In this paper, we prove a formula, realizing certain residual Eisenstein series on symplectic groups as regularized kernel integrals. These...
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Ramanujan’s hyperelliptic inversion formula
We present a direct proof of an inversion formula for a hyperelliptic integral recorded by Ramanujan in his second notebook.
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Operator-Norm Trotter Product Formula on Banach Spaces
Here we collect results concerning the operator-norm convergent Trotter product formula for...
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Bernstein–Riemann Interpolation Formula for Arbitrary Continuous Functions on an Interval
AbstractFor arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on...
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A Bessel Analog of the Riesz Composition Formula
We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the...
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Voronovskaja formula for Aldaz–Kounchev–Render operators: uniform convergence
The Voronovskaja formula for Aldaz–Kounchev–Render operators was established in terms of pointwise convergence. For suitable functions we prove it...
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Improved Quadrature Formula for a Single-Layer Potential
AbstractAn improved quadrature formula is derived for a single-layer potential with a smooth density given on a closed or open surface. The formula...
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Applying A.G. Postnikov’s Formula in Algebraic Number Fields
AbstractWe present a new result on the generalisation of A.G. Postnikov’s formula to the case of powers of 2. This, together with the original work...
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On Popov’s explicit formula and the Davenport expansion
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series...
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Generalized Poisson Formula for Second Order Elliptic Systems
In the unit disc, we consider the Dirichlet problem for second order elliptic system with only higher order constant coefficients. We establish the...
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Self-duality, Pieri Formula and Cauchy Formulas
Self-duality (evaluation symmetry), which we are going to discuss below, is one of the most characteristic properties of Macdonald polynomials. In...