A Generalization of the Angle Doubling Formulas for Trigonometric Functions

Gaston Brouwer

doi:10.4169/math.mag.90.1.12

A Generalization of the Angle Doubling Formulas for Trigonometric Functions

Mathematics Magazine ◽

10.4169/math.mag.90.1.12 ◽

2017 ◽

Vol 90 (1) ◽

pp. 12-18

Author(s):

Gaston Brouwer

Keyword(s):

Trigonometric Functions

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

International Journal of Applied Evolutionary Computation ◽

10.4018/jaec.2013040102 ◽

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.

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

Journal of Mathematical Chemistry ◽

10.1007/s10910-021-01282-y ◽

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.

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