Recurrent sequences and the measure of irrationality of values of elliptic integrals

1997 ◽  
Vol 61 (5) ◽  
pp. 657-661
Author(s):  
V. V. Zudilin
Keyword(s):  
Elliptic Integrals ◽  
Recurrent Sequences ◽  
Measure Of Irrationality

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

Recurrent sequences and endomorphisms of Euclidean spaces

1994 ◽  
Vol 63 (1) ◽  
pp. 92-96
Author(s):  
Lutz Lucht ◽  
Cordelia Methfessel
Keyword(s):  
Euclidean Spaces ◽  
Recurrent Sequences

Some Applications of Elliptic Integrals of First Kind

2013 ◽  
Vol 65 (1) ◽  
Author(s):  
Yasamin Barakat ◽  
Nor Haniza Sarmin
Keyword(s):  
Algebraic Function ◽  
High Accuracy ◽  
Elliptic Integrals ◽  
Definite Integrals ◽  
Engineering Mathematics ◽  
Optimal Values ◽  
Complete Elliptic Integrals

One of the most important applications of elliptic integrals in engineering mathematics is their usage to solve integrals of the form  (Eq. 1), where  is a rational algebraic function and  is a polynomial of degree  with no repeated roots. Nowadays, incomplete and complete elliptic integrals of first kind are estimated with high accuracy using advanced calculators.  In this paper, several techniques are discussed to show how definite integrals of the form (Eq. 1) can be converted to elliptic integrals of the first kind, and hence be estimated for optimal values. Indeed, related examples are provided in each step to help clarification.

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