Search Maps.com

 Channel Features
 Travel Deals Travel Alert Bulletin Travel Tools Business Traveler Guide Student Traveler Guide Map & Travel Store

 Get travel news, alerts, tips, deals, and trivia delivered free to your email in-box. Email Address: tell me more

 Site Tools
 Site Map About Maps.com Contact Maps.com Advertise with Maps.com Affiliate Program Order Tracking View Cart Check Out Help

 Site Map | Help | Home
 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: 21. Spheroidal Wave Functions Mathematical Properties 21.1. Definition of Elliptical Coordinates i 21.1.1 rl and r2 are the distances to the foci of a family of confocal ellipses and hyperbolas; 2 j is the dis- tance between foci. 21.1.2 a=f[, b = j m - r , e=- f a a=semi-major axis; b=semi-minor axis; e=ec- centricity . Equation of Family of Confocal Ellipses x2 Ye -f" 21.1.3 -p\$gq- Equation of Family of Confocal Hyperbolas _--- x2 Y2 , - j Z 21.1.4 q2 1-7 Relations Between Cartesian and Elliptical Coordinates 21.1.5 x=ftq; y=fJ(s2-l)(1-q2) 21.2. Definition of Prolate Spheroidal Coordinates If the system of confocal ellipses and hyberbolas referred to in 21.1.3 and 21.1.4 revolves around the major axis, then 2 2 1.2 2 2 Ta (2 52-1 q2 1-7 21.2.1 -+-=f"; ----- 2-j2 y = r cos Ip; z=r sin Ip; 0