IX. Infinite Series of Functions

1947 ◽  
pp. 48-50
Keyword(s):  
Infinite Series ◽  
Series Of Functions

scholarly journals XIV. On the convergence of infinite series of analytic functions

1905 ◽  
Vol 204 (372-386) ◽  
pp. 481-497
Keyword(s):  
Analytic Function ◽  
General Theory ◽  
Infinite Series ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Point Of View ◽  
General Point ◽  
Associated Functions ◽  
Linear Differential ◽  
Series Of Functions

In the first section of the following work an attempt is made to deal with the convergence of infinite series of functions defined by linear differential equations of the second order from the most general point of view. Functions of Lamé Bessel and Legendre are considered as examples. In the second section the results obtained are applied to the expansion of an arbitrary uniform analytic function of an arbitrary uniform analytic function of z in a series of hypergeometric functions, and the expansion is shown to be valid if the function is regular within a certain ellipse in the z -plane. An expansion in a series of Legendre’s associated functions is deduced by a transformation. The method has been applied by the writer to other cases, but the foregoing offer adequate illustration of the general theory.

Differentiation of Infinite Series of Functions

1959 ◽  
Vol 66 (10) ◽  
pp. 890
Author(s):  
R. W. Bagley
Keyword(s):  
Infinite Series ◽  
Series Of Functions

Infinite Series of Functions

2017 ◽  
pp. 443-476
Author(s):  
Lawrence J. Corwin ◽  
Robert H. Szczarba
Keyword(s):  
Infinite Series ◽  
Series Of Functions

Toroidal Helical Fields

1987 ◽  
Vol 42 (10) ◽  
pp. 1124-1132 ◽  
Author(s):  
M. Y. Kucinski ◽  
I. L. Caldas
Keyword(s):  
Coordinate System ◽  
Infinite Series ◽  
Plasma Column ◽  
Scalar Potential ◽  
Laplace’S Equation ◽  
Laplace's Equation ◽  
Small Curvature ◽  
Partial Sum ◽  
Magnetic Surfaces ◽  
Series Of Functions

Using the conventional toroidal coordinate system Laplace’s equation for the magnetic scalar potential due to toroidal helical currents is solved. The potential is written as a sum of an infinite series of functions. Each partial sum represents the potential within some accuracy. The effect of the winding law is analysed in the case of small curvature. Approximate magnetic surfaces formed by toroidal helical currents flowing around a standard tokamak chamber are determined. Stability of the plasma column in this system against displacements is discussed.

Some Infinite Series of 2-Weighing and 3-Weighing Matrices from Hadamard Matrices

2018 ◽  
Vol 9 (12) ◽  
pp. 2165-2168
Author(s):  
Gopal Prajapati ◽  
Mithilesh Kumar Singh
Keyword(s):  
Infinite Series ◽  
Hadamard Matrices ◽  
Weighing Matrices
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