Symbolic summation

2013 ◽  
pp. 645-676
Author(s):  
Joachim von zur Gathen ◽  
Jurgen Gerhard
Keyword(s):  
Symbolic Summation

scholarly journals -Analogues of Symbolic Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Michael J. Dancs ◽  
Tian-Xiao He
Keyword(s):  
Linear Operators ◽  
Derivative Operator ◽  
Symbolic Summation ◽  
Series Transformation ◽  
Transformation Formulas ◽  
Symbolic Substitution

Here presented are -extensions of several linear operators including a novel -analogue of the derivative operator . Some -analogues of the symbolic substitution rules given by He et al., 2007, are obtained. As sample applications, we show how these -substitution rules may be used to construct symbolic summation and series transformation formulas, including -analogues of the classical Euler transformations for accelerating the convergence of alternating series.

A symbolic summation approach to feynman integrals

2011 ◽  
Vol 44 (3/4) ◽  
pp. 95-96
Author(s):  
Johannes Blümlein ◽  
Sebastian Klein ◽  
Carsten Schneider ◽  
Flavia Stan
Keyword(s):  
Feynman Integrals ◽  
Symbolic Summation

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

2013 ◽  
Vol 11 (4) ◽  
Author(s):  
Irina Georgieva ◽  
Clemens Hofreither ◽  
Christoph Koutschan ◽  
Veronika Pillwein ◽  
Thotsaporn Thanatipanonda
Keyword(s):  
Harmonic Function ◽  
Finite Number ◽  
Interpolation Problem ◽  
Numerical Experiments ◽  
Regular Polygon ◽  
Harmonic Polynomial ◽  
Regular Polygons ◽  
Symbolic Summation ◽  
Radon Projections ◽  
Harmonic Interpolation

AbstractGiven 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.

scholarly journals Telescoping in the context of symbolic summation in Maple

2004 ◽  
Vol 38 (4) ◽  
pp. 1303-1326 ◽  
Author(s):  
S.A. Abramov ◽  
J.J. Carette ◽  
K.O. Geddes ◽  
H.Q. Le
Keyword(s):  
Symbolic Summation
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