Browsing Faculty Scholarship by Subject "Elliptical arc length"

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An Inequality Involving the Generalized Hypergeometric Function and the Arc Length of an Ellipse

Richards, Kendall C. (Siam Journal on Mathematical Analysis, 2000)

In this paper we verify a conjecture of M. Vuorinen that the Muir approxima- tion is a lower approximation to the arc length of an ellipse. Vuorinen conjectured that f(x) = 2F1( 1 2 , − 1 2 ; 1; x) − [(1 + (1 − ...
A Monotonicity Property Involving 3F2 and Comparisons of the Classical Approximations of Elliptical Arc Length

Richards, Kendall C. (Siam Journal on Mathematical Analysis, 2001)

Conditions are determined under which 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) is a monotone function of n satisfying ab· 3F2 (−n, a, b; a + b + 2, ε − n + 1; 1) ≥ ab· 2F1 (a, b; a + b + 2; 1) . Motivated by a conjecture ...

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