New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: 17. Elliptic Integrals L. M. MILNE-THOMSON Contents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 17.1. Definition of Elliptic Integrals . . . . . . . . . . . . . 17.2. Canonical Forms . . . . . . . . . . . . -. . . . . . . 17.3. Complete Elliptic Integrals of the First and Second Kinds . . 17.4. Incomplete Elliptic Integrals of the First and Second Kinds . 17.5. Landen’s Transformation . . . . . . . . , . . . . . . . 17.6. The Process of the Arithmetic-Geometric Mean . . . . . . 17.7. Elliptic Integrals of the Third Kind . . . . . . . . . . . Numerical Methods . . . . . . . . . . . . . . . .* . . . . . . 17.8. Use and Extension of the Tables . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Table 17.1. Complete Elliptic Integrals of the First and Second Kinds and the Nome p With Argument the Parameter m . . . . . . . . . K(m), K’(m), 15D; dm), ni(m), 15D; E(m), E’(m), 9D m= 0(.01) 1 Table 17.2. Complete Elliptic Integrals of the First and Second Kinds and the Nome p Withhgument the Modular Angle (Y . . . . . . K ( 4 , K ’ ( 4 , m, a l ( 4 , ma), E’(4, a= OO( 1 0)90° 15D Table 17.3. Parameter m With Argument K’(m)/K(m) . . . . . . . K’(m)/K(m)= .3(.02)3, 10D Table 17.4. Aulriliary Functions for Computation of the Nome q and the Parameter m. , . . . . . . . . . . . . . . . . . . . . . . . Q(m) =pi (m)/mi 15D ml=O( .O1). 15 Table 17.5. Elliptic Integral of the First Kind F(lp\a) . . . . . . . a=0°(20)900, 5°(100)850, ( ~ = 0 ~ ( 5 ~ ) 9 0 ~ , 8D Table 17.6. Elliptic Integral of the Second Kind E(q\a) . . . . . . a=0°(20)900, 5°(100)850, q=0°(50)900, 8D Page 589 589 589 590 592 597 598 599 600 600 606 608 610 6 12 612 613 616 1 University of Arizona. (Prepared under contract with the National Bureau of StIbdUde.) 587 The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States. ©2000 ConvertIt.com, Inc. All rights reserved. Terms of Use.