From: William Lee Irwin III Subject: Re: help:elliptic integral Date: Fri, 29 Dec 2000 01:17:36 GMT Newsgroups: sci.math,sci.math.num-analysis Summary: [missing] Stevanus Budi Waluya schrieb in im Newsbeitrag: 3A3F79C9.C9098516@dv.twi.tudelft.nl... > Dear all, > I have a problem to solve a general elliptic integral in analytically. The > problem is int((2*k-(9*r^2+2*lambda/3*r^3+beta/2*r^4))^(-1/2),r=0..x), where > k > is a constant. I tried to solve by expressing the problem into general form > but > still not success yet. Is it possible to solve analytically? > Any help would be greatly appreciated. > Thank You! > stevanus@dv.twi.tudelft.nl Yes, elliptic integrals are very doable in analytical terms. It's not a commonly covered topic in modern calculus texts, but late 19th century and early 20th century texts do in fact cover this in detail. I myself learned the technique from Whittaker & Watson, "A Course in Modern Analysis" (which is still in print), and have a demonstration of the technique (which is part of a work in progress) in various formats at the following URLs: http://holomorphy.com/integration/integration.latex http://holomorphy.com/integration/integration.dvi http://holomorphy.com/integration/integration.ps http://holomorphy.com/integration/integration.pdf It is the concluding example, though I'm hard-pressed to extract the section or page number from where I am now. One perhaps slightly unusual aspect of my presentation is that I use inverse Jacobi elliptic functions instead of the more usual Legendre elliptic integrals. Any corrections (to any part of the above) are welcome. I do already know that there are necessary side conditions I am omitting from some of the derivations. Cheers, Bill -- A mathematician is a system for turning coffee into theorems. -- Paul Erdös A comathematician is a system for turning theorems into coffee. -- Tim Poston jhicks: A Sun marketroid is a system for turning coffee into programming languages. =)