Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic

2008 ◽  
Vol 105 (1-3) ◽  
pp. 245-260 ◽  
Author(s):  
Toshio Fukushima
Keyword(s):  
Elliptic Functions ◽  
Elliptic Integrals ◽  
Fast Computation ◽  
Jacobian Elliptic Functions ◽  
Incomplete Elliptic Integrals

Vector Potential and Magnetic Field of Current-carrying Finite Elliptic Arc Segment in Analytical Form

1985 ◽  
Vol 40 (11) ◽  
pp. 1069-1074 ◽  
Author(s):  
L. Urankar
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Elliptic Functions ◽  
Analytical Form ◽  
Efficient Computation ◽  
Jacobian Elliptic Functions ◽  
Arbitrary Length ◽  
Computation Algorithm ◽  
Incomplete Elliptic Integrals ◽  
Analytical Expressions

Analytical expressions for the components of the vector potential and magnetic field of a current-carrying elliptic arc filament of arbitrary length are derived. All the expressions developed consist of only known functions such as Jacobian elliptic functions, complete and incomplete elliptic integrals of the first, second and third kind, and thus permit a compact timesaving efficient computation algorithm.

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