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Full-Text Articles in Physical Sciences and Mathematics
On The Trigonometric Expansion Of Elliptic Functions, M. A. Basoco
On The Trigonometric Expansion Of Elliptic Functions, M. A. Basoco
Department of Mathematics: Faculty Publications
The problem of expressing an elliptic function in terms of infinite sums of trigonometric functions has been treated by Hermite, Briot and Bouquet, A. C. Dixon and others. In the present paper we treat the same problem from the point of view of Cauchy's residue theorem in function theory, which is also Briot and Bouquet's starting point, but we differ from these authors in that the integrand we use leads to an expansion for an elliptic function which is valid in an arbitrarily wide, but finite, strip of the complex plane, and which contains certain classical results as special cases. …
Parametric Solutions Of Certain Diophantine Equations, T. A. Pierce
Parametric Solutions Of Certain Diophantine Equations, T. A. Pierce
Department of Mathematics: Faculty Publications
In this note parametric solutions of certain diophantine equations are given. The method of obtaining the solutions is derived from an equation involving the determinants of certain matrices. It will be recognized that the method is a generalization of the method of Euler and Lagrange which depends on forms which repeat under multiplication. The matrices used in this paper must be such that their forms are retained under matric multiplication and addition. When integer values are assigned to the parameters of our solutions we obtain integer solutions of the particular equation under consideration; however not all integer solutions are necessarily …
A Certain Multiple-Parameter Expansion, H. P. Doole
A Certain Multiple-Parameter Expansion, H. P. Doole
Department of Mathematics: Faculty Publications
C. C. Camp has shown the convergence of the expansion of an arbitrary function in terms of the solutions of the systems of equations
X1’ (λa1 - Σi=2nμi)X1 = 0,
X1’ (λai + μi)Xi = 0, (j = 2, 3, …, n),
where the ai’s are functions of x, with the boundary conditions
Xi(-π) = Xi(π), (j = 1, 2, …, n).
In this paper it is intended to use a …