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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: 806 BERNOULLI AND EULER POLYNOMIALS, RIEMANN ZETA FUNCTION Symbolic Operations 23.1.25 p(B(z) + 1 ) - ~ ( B ( z ) ) = p ' ( ~ ) 23.1.26 B,(z+h)=(B(z)+h)" n=O, 1 , . . . Here p ( z ) denotes a polynomial in z and after expanding we set (B(z)}"=B,(z) and (E(Z)}~=E,(Z). Relations Between the Polynomials 23.1.27 23.1.28 n=2,3, . 23.1.29 Euler-Maclaurin Formulas Let F(z) have its fmt 2n derivatives continuous on an interval (a, a). Divide the interval into m equal parts and let h=(b-a)/m. Then for some 0, i>e>o, depending on FZn)(z) on (a, b), we have 23.1.30 k= 5 0 F(a+ kh) =f l F(t)dt+i# { F(b) +F(u) } Equivalent to this is 23.1.31 A Let B&) =B,(z--4). The Euler Summation Formula is 23.1.32 m-1 k=O C F(a+kh+wh)=; l F ( t ) d t p 52n, 12 w>O 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.