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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: 20. Mathieu Functions GERTRUDE BLANCH Contents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 20.1. Mathieu’s Equation . . . . . . . . . . . . . . . . . 20.2. Determination of Characteristic Values , . . . . . . . . 20.3. Floquet’s Theorem and Its Consequences . . . . . . . . 20.4. Other Solutions of Mathieu’s Equation . , . . . . . . . 20.5. Properties of Orthogonality and Normalization . . . . . . 20.6. Solutions of Mathieu’s Modified Equation for Integral Y . , 20.7. Representations by Integrals and Some Integral Equations . 20.8. Other Properties . . . . . . . . . . . . . . . . . . . 20.9. Asymptotic Representations . . . . . . . . . . . . . . 20.10. Comparative Notations . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Table 20.1. Characteristic Values, Joining Factors, Some Critical Values ( O < q < m ) . . . . . . . . . . . . . , . . . . . . . Even Solutions Odd Solutions q=0(5)25, 8D or S ar+2q-(4~+2) &, br+2q-(4~-2) h q-f=. 16 (- .04) 0, 8D T=O, 1, 2, 5, 10, 15 Table 20.2. Coefficients A, and B, . . . . . . . . . . . . . . . q=5, 25; T=O, 1, 2, 5, 10, 15, 9D 1 Aeronautical Research Laboratories, Wright-Patterson Air Force Base, Ohio. Page 722 722 722 72 7 730 732 732 735 73 8 740 744 74 5 748 750 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.