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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: BERNOULLI AND EULER POLYNOMIALS, RIEMA" ZETA FUNCTION 805 Integrals m,n=O, 1,. . . I (The polynomials are orthogonal for m+n odd.) Inequalities 23.1.13 IBznl>(Bzn(~)l n=1, 2, . . ., 23.1.14 n=1,2,. . ., \$>X>O 23.1.15 n==1,2,. . . 4-nlE2,1>(-l)fiEz,(x)>o n=1,2, . . ., ;>z>o 4(2n- 1) ! (1 +2q)> 1 (- 1) "E2, - 1 (4 >o a 2 n n=1,2,. . ., +>x>O n=O,l,. . . Fourier Expansions I 23.1.16 n! cos (2?rkx-\$nn) kn B,(x)=-2 -, c ( 2 r ) k = l 23.1.17 n>O, 1 2 x 2 0 n=O, 1>x>o I 23.1.18 (-1)"-'2(2n)! cos 2kax ( 2 7 p k = l kZn 2 Bzn (2) = n=1,2,. . ., l>z>O Special Values 23.1.19 B2,+1=0 n=1,2,. . . = B, n=O,l,. . . 23.1.20 23, (0) = (- 1) "B, (1) 23.1.21 B,(+)=-(I -2'-'9 B, n=O,l,. . . n>o,1>x20 n=o, 1>2>0 En (8) = 2 -"En 72=0,1,. . . 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.