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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 | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: 23. Bernoulli and Euler Polynomials- Riemann Zeta Function EMILIE V. HAYNSWORTH AND KARL GOLDBERG !L Con tents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 804 Formula . . . . . . . . . . . . . . . . . . . . . . 804 Powers . . . . . . . . . . . . . . . . . . . . . . . 807 References . . . . . . . . . . . . . . . . . . . . . . . . . . 808 Table 23.1. Coefficients of the Bernoulli and Euler Polynomials 809 Table 23.2. Bernoulli and Euler Numbers . . . . . . . . . . . . . Table 23.3. Sums of Reciprocal Powers . . . . . . . . . . . . . . Page 23.1. Bernoulli and Euler Polynomials and the Euler-Maclaurin 23.2. Riemann Zeta Function and Other Sums of Reciprocal . . . B,(x) and E,(x), n=0(1)15 B, and En, n=O, 1, 2(2)60, Exact and B, to 10s 810 811 m i m 1 n= 1 (1)42 Table 23.4. Sums of Positive Powers . . . . . . . . . . . . . . . 813 m k =1 c k",n=1(1)10, m=1(1)100 Table 23.5. xn/n!, x=2(1)9, n=1(1)50, 10s . . . . . . . . . . . . 818 The authors acknowledge the assistance of Ruth E. Capuano in the preparation and checking of the tables. 1 National Bureau of Standards. 2 National Bureau of Standards. (Presently, Auburn University.) 803 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.