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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: 22 . Orthogonal Polynomials URS W . HOCHSTRASSER Con tents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 22.1. Definition of Orthogonal Polynomials 22.2. Orthogonality Relations . . . . . . . . . . . . . . . . 22.3. Explicit Expressions . . . . . . . . . . . . . . . . . . 22.4. Special Values . . . . . . . . . . . . . . . . . . . . . 22.5. Interrelations . . . . . . . . . . . . . . . . . . . . . 22.6. Differential Equations . . . . . . . . . . . . . . . . . 22.7. Recurrence Relations . . . . . . . . . . . . . . . . . 22.8. Differential Relations . . . . . . . . . . . . . . . . . 22.9. Generating Functions . . . . . . . . . . . . . . . . . 22.10. Integral Representations . . . . . . . . . . . . . . . . . . . . . . . . . 22.11. Rodrigues’ Formula . . . . . . . . . . . . . . . . . . 22.12. Sum Formulas . . . . . . . . . . . . . . . . . . . . 22.13. Integrals Involving Orthogonal Polynomials . . . . . . . 22.14. Inequalities . . . . . . . . . . . . . . . . . . . . . 22.15. Limit Relations . . . . . . . . . . . . . . . . . . . 22.16. Zeros . . . . . . . . . . . . . . . . . . . . . . . 22.17. Orthogonal Polynomials of a Discrete Varihble . . . . . . Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 22.18. Use and Extension of the Tables . . . . . . . . . . . . 22.19. Least Square Approximations . . . . . . . . . . . . . 22.20. Economization of Series . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Table 22.1. Coefficients for the Jacobi Polynomials PFB)(x) . . . . . Table 22.2. Coefficients for the Ultraspherical Polynomials CF) (2) and for xn in Terms of (72) (2) . . . . . . . . . . . . . . . . . . . . Table 22.3. Coefficients for the Chebyshev Polynomials Tn(z) and for . . . . . . . . . . . . . . . . . . . . . n=0(1)6 n=0(1)6 zn in Terms of T, (z) n=0(1)12 Table 22.4. Values of the Chebyshev Polynomials Tn(z) . . . . . . . n=0(1)12. x=.2(.2)1, 1OD Table 22.5. Coefficients for the Chebyshev Polynomials Un(z) and for P i n Terms of U, (z) . . . . . . . . . . . . . . . . . . . . n=0(1)12 n=0(1)12. 2=.2(.2)1, 10D 1 Guest Worker. National Bureau of Standards. from The American University . 771 Table 22.6. Values of the Chebyshev Polynomials U, (x) . . . . . . ently. Atomic Energy Commission. Switzerland.) Page 773 773 774 775 777 777 781 782 783 783 784 785 785 785 786 787 787 788 788 788 790 791 792 793 794 795 795 796 796 (Pres- 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.