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An extension of the method of brackets. Part 1

100%

Gonzalez I., Kohl K., Jiu L., Moll V. H.

Open Mathematics

2017

tom 15

nr 1

1181-1211

The method of brackets is an efficient method for the evaluation of alarge class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the concepts of null and divergent series. These are formal representations of functions, whose coefficients an have meromorphic representations for n ∈ ℂ, but might vanish or blow up when n ∈ ℕ. These ideas are illustrated with the evaluation of a variety of entries from the classical table of integrals by Gradshteyn and Ryzhik.

Harmonic interpolation based on Radon projections along the sides of regular polygons

64%

Georgieva I., Hofreither C., Koutschan C., Pillwein V., Thanatipanonda T.

Open Mathematics

2013

tom 11

nr 4

609-620

Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.

Ograniczanie wyników

2 Open Mathematics

1 Georgieva I.

1 Gonzalez I.

1 Hofreither C.

1 Jiu L.

1 Kohl K.

1 Koutschan C.

1 Moll V. H.

1 Pillwein V.

1 Thanatipanonda T.

1 2017

1 2013

Wyniki wyszukiwania

An extension of the method of brackets. Part 1

Harmonic interpolation based on Radon projections along the sides of regular polygons