scholarly journals Analytic continuation of generalized trigonometric functions

2021 ◽  
Author(s):  
Pisheng Ding
Keyword(s):  
Analytic Continuation ◽  
Trigonometric Functions

A New Solution for Maxterm Problem in Trigonometric Functions by Simulated Annealing Algorithm

2013 ◽  
Vol 4 (2) ◽  
pp. 20-28
Author(s):  
Farhad Soleimanian Gharehchopogh ◽  
Hadi Najafi ◽  
Kourosh Farahkhah
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Trigonometric Functions ◽  
Matlab Software ◽  
Annealing Algorithm ◽  
Do So

The present paper is an attempt to get total minimum of trigonometric Functions by Simulated Annealing. To do so the researchers ran Simulated Annealing. Sample trigonometric functions and showed the results through Matlab software. According the Simulated Annealing Solves the problem of getting stuck in a local Maxterm and one can always get the best result through the Algorithm.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

On the Rational Values of Trigonometric Functions of Angles that Are Rational in Degrees

2021 ◽  
Vol 94 (2) ◽  
pp. 132-134
Author(s):  
Bonaventura Paolillo ◽  
Giovanni Vincenzi
Keyword(s):  
Trigonometric Functions

scholarly journals Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions

2005 ◽  
Vol 614 (1-2) ◽  
pp. 53-61 ◽  
Author(s):  
Johannes Blümlein ◽  
Sven-Olaf Moch
Keyword(s):  
Analytic Continuation ◽  
Anomalous Dimensions

scholarly journals Spectral Inclusion and Analytic Continuation

1999 ◽  
Vol 31 (6) ◽  
pp. 722-728 ◽  
Author(s):  
A. Atzmon ◽  
A. Eremenko ◽  
M. Sodin
Keyword(s):  
Analytic Continuation ◽  
Spectral Inclusion
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