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• Elliptic_rational_functions abstract "In mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic electronic filters. (These functions are sometimes called Chebyshev rational functions, not to be confused with certain other functions of the same name).Rational elliptic functions are identified by a positive integer order n and include a parameter ξ ≥ 1 called the selectivity factor. A rational elliptic function of degree n in x with selectivity factor ξ is generally defined as: cd is the Jacobi elliptic cosine function. K is a complete elliptic integral of the first kind. is the discrimination factor, equal to the minimum value of the magnitude of for .For many cases, in particular for orders of the form n = 2a3b where a and b are integers, the elliptic rational functions can be expressed using algebraic functions alone. Elliptic rational functions are closely related to the Chebyshev polynomials: Just as the circular trigonometric functions are special cases of the Jacobi elliptic functions, so the Chebyshev polynomials are special cases of the elliptic rational functions.".
• Elliptic_rational_functions thumbnail Rational_Elliptic_Functions_(n=1,2,3,4,_x=--1,1-).svg?width=300.
• Elliptic_rational_functions wikiPageExternalLink EllipticRationalFunction.html.
• Elliptic_rational_functions wikiPageID "6266055".
• Elliptic_rational_functions wikiPageRevisionID "600412270".
• Elliptic_rational_functions hasPhotoCollection Elliptic_rational_functions.
• Elliptic_rational_functions subject Category:Elliptic_functions.
• Elliptic_rational_functions subject Category:Rational_functions.
• Elliptic_rational_functions type Abstraction100002137.
• Elliptic_rational_functions type EllipticFunctions.
• Elliptic_rational_functions type Function113783816.
• Elliptic_rational_functions type MathematicalRelation113783581.
• Elliptic_rational_functions type RationalFunctions.
• Elliptic_rational_functions type Relation100031921.
• Elliptic_rational_functions comment "In mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic electronic filters. (These functions are sometimes called Chebyshev rational functions, not to be confused with certain other functions of the same name).Rational elliptic functions are identified by a positive integer order n and include a parameter ξ ≥ 1 called the selectivity factor.".
• Elliptic_rational_functions label "Elliptic rational functions".
• Elliptic_rational_functions label "Rational elliptische Funktionen".
• Elliptic_rational_functions label "楕円有理関数".
• Elliptic_rational_functions sameAs Rational_elliptische_Funktionen.
• Elliptic_rational_functions sameAs 楕円有理関数.
• Elliptic_rational_functions sameAs m.0fzp1m.
• Elliptic_rational_functions sameAs Q2132775.
• Elliptic_rational_functions sameAs Q2132775.
• Elliptic_rational_functions sameAs Elliptic_rational_functions.
• Elliptic_rational_functions wasDerivedFrom Elliptic_rational_functions?oldid=600412270.
• Elliptic_rational_functions depiction Rational_Elliptic_Functions_(n=1,2,3,4,_x=--1,1-).svg.
• Elliptic_rational_functions isPrimaryTopicOf Elliptic_rational_functions.