116. The Cosine Rule and the Addition Formula

1964 ◽  
Vol 48 (366) ◽  
pp. 423
Author(s):  
M. W. Green
Keyword(s):  
Addition Formula

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

The four basic errors of special theory of relativity and the solution offered by extended Galilean relativity

2020 ◽  
Vol 33 (2) ◽  
pp. 211-215 ◽  
Author(s):  
Shukri Klinaku
Keyword(s):  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Addition Formula ◽  
Principle Of Relativity ◽  
Galilean Relativity ◽  
Velocity Addition ◽  
Basic Equations ◽  
Tycho Brahe

Is the special theory of relativity (STR) a “simple” or “tricky” theory? They who think that it is a simple theory say (i) that its postulates are simple, that Nature is such, (ii) that the mathematics of STR is perfect, and (iii) that experiments support it. I consider its two postulates to be very true, whereas the mathematics of the STR has a shortcoming, and, as for the experiments, the question must be posed: which theory do they support best? The problem for STR lies in the transition from its postulates to its basic equations, i.e., Lorentz transformation and the velocity addition formula. The passage from the principle of relativity and the constancy of the speed of light to the basic equations of the STR is affected by four fundamental errors—three physical and one mathematical. Continuous attempts to reconcile these latent mistakes have made STR increasingly tricky. As a result, it is in a similar situation to Ptolemy's geocentric model after “improvements” thereto by Tycho Brahe. However, the “Copernican solution” for relative motion—offered by extended Galilean relativity—is very simple and effective.

Recasting the Lorentz Velocity Addition Formula

2010 ◽  
Vol 48 (1) ◽  
pp. 4-4
Author(s):  
John Mallinckrodt
Keyword(s):  
Addition Formula ◽  
Velocity Addition

x-only point addition formula and faster compressed SIKE

2020 ◽  
Author(s):  
Geovandro Pereira ◽  
Javad Doliskani ◽  
David Jao
Keyword(s):  
Addition Formula

scholarly journals Addition Formula and Related Integral Equations for Heine—Stieltjes Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1231
Author(s):  
Hans Volkmer
Keyword(s):  
Integral Equations ◽  
Explicit Form ◽  
Spherical Harmonics ◽  
Reproducing Kernel ◽  
Addition Formula ◽  
Symmetric Products ◽  
Special Cases ◽  
Related Integral ◽  
Generalized Spherical Harmonics ◽  
The Relationship

It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and from the known explicit form of the reproducing kernel of these spaces. In special cases, the addition formula is written out explicitly and verified. As an application, integral equations for Heine–Stieltjes quasi-polynomials are found.

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