Browsing by Author "Ayana Mossie"

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    Some Applications of Elliptic Functions and Elliptic Integrals
    (Addis Ababa University, 2024-09) Ayana Mossie; Bahru Tsegaye
    One of the most important applications of elliptic integrals of the form ∫𝑅(𝑥.√𝑝𝑛(x)) dx where R is rational algebraic function and 𝑝𝑛(x) is polynomials of degree 3 or 4 with no repeated roots. Nowadays, incomplete and complete elliptic integrals of the first kind are estimated with high accuracy using advanced calculators. In this paper, several techniques are discussed to show how definite integrals of the form ∫𝑅(𝑥.√𝑝𝑛(x)) dx can be converted to elliptic integrals of the first kind, and hence be estimated for optimal values. Indeed examples are provided in each step to help clarifications. Finally I have used eq.6 and eq.23 which is an important equations to show my analysis of ascending and descending transformation by taking initial values of F(∅0,k0) to provide a 30 decimal place values of numerical evaluations.