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 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 | MEDIUM | LARGE Below is the OCR-scanned text from this page: 21. Spheroidal Wave Functions ARNOLD N. LOWAN Contents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 21.1. Definition of Elliptical Coordinates . . . . . . . . . . 21.2. Definition of Prolate Spheroidal Coordinates . . . . . . 21.3. Definition of Oblate Spheroidal Coordinates . . . . . . . 21.4. Laplacian in Spheroidal Coordinates . . . . . . . . . . 21.5. Wave Equation in Prolate and Oblate Spheroidal Coordinates 21.6. Differential Equations for Radial and Angular Spheroidal Wave Functions . . . . . . . . . . . . . . . . . . 21.7. Prolate Angular Functions . . . . . . . . . . . . . . 21.8. Oblate Angular Functions . . . . . . . . . . . . . . 21.9. Radial Spheroidal Wave Functions . . . . . . . . . . 21.10. Joining Factors for Prolate Spheroidal Wave Functions . 21.11. Notation . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Table 21.1. Eigenvalues-Prolate and Oblate . . . . . . . . . . . m=0(1)2, n=m(l)m+4 c2=0(1) 16, c - ~ = .25( - .Ol)O, 4-6D Table 21.2. Angular Functions-Prolate and Oblate . . . . . . . . m=0(1)2, n=m(1)3, q=O(.l)l O=Oo(100)900, ~=1(1)5, 2-4D Table 21.3. Prolate Radial Functions-First and Second Kinds . . . m=0(1)2, n=m(1)3 (=1.005, 1.02, 1.044, 1.077, ~=1(1)5, 4 s Table 21.4. Oblate Radial Functions-First and Second Kinds . . . . m=O, I, n=m(l)m+2; m, n=2 ( = O , .75, c=.2, .5, .8, 1(.5)2.5, 5s Table 21.5. Prolate Joining Factors-First Kind . . . . . . . . . . m=O, 1, n=m(l)m+2; m, n=2 ~=1(1)5, 4 s Page 752 752 752 752 752 752 753 753 756 756 757 758 759 760 766 768 769 769 1 Yeshiva University. (Prepared under contract with the National Bureau of S tandarde.) (Deceased.) 751 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.