Application of singular elliptic functions to the investigation of certain properties of Legendre polynomials
Authors:
Abstract
In this work, the following theorem is proved. Let m be a negative integer containing no square divisors. Consider the quadratic field k(√m) and let ω1, ω2 be a basis of some ideal of this field, with the imaginary part of the ratio ω2/ω1 being positive. Furthermore, let ρ(u; ω1, ω2, ω3) be the well-known Weierstrass function (in what follows we will index the basis ω1, ω2 such that the ratio ω2/ω1 has a positive imaginary part), which satisfies the following differential equation
Область исследования:
(Archived) Articles
Funding:
None
References
- R. Fueter. Vorlesungen über die singulären Moduln und die komplexe Multiplikation der elliptischen Funktionen. Berlin 1924, 1927.
- Tannery et Molk. Éléments de la théorie des fonctions elliptiques 1902. V. IV. p. 91.
- H. Weber. Elliptische Funktionen und algebraische Zahlen. 1908. Table VI.
Similar articles
The curve of the solubility of copper in aluminum in solid state
1929 P. Ya. Sal'dau, N. G. Anisimov
Acetyl chloride, sulfuryl chloride and monochloroacetic acid. The process of obtaining them in large quantities by laboratory methods
1929 A. K. Boldyrev