tailieunhanh - Handbook of mathematics for engineers and scienteists part 147

Handbook of mathematics for engineers and scienteists part 147. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | 990 Special Functions and Their Properties . Generating function. Fourier series expansions. Integrals. The generating function is expressed as . Enx lt n . el 1 n n 0 This relation may be used as a definition of the Euler polynomials. Fourier series expansions E x 4-nf. f À i 7n n 0 0 x 1 n 0 0 x 1 nv 7 n i x 2k 1 n i v n 2n sin 2fc 1 nx E2n x 4 -1 nn rE 2k 1 2n r n 0 0 x 1 n 0 0 x 1 k 0 v 2n - 1 cos 2fc 1 nx E2n-1 x 4 -1 I n2n E 2k 1 2n n 2 0 X Integrals f E t dt E 1 X - E .Jn n 1 a f Em t En t dt 4 -1 n 2m n 2 - 1 m n Bm n 2 J0 m n 2 where m n 0 1 . and Bn are Bernoulli numbers. The Euler polynomials are orthogonal for even n m. Connection with the Bernoulli polynomials E 1 x 21 IbT 1 - B X 1 2 ÎBn X -2n B 1. n L 2 2 J n V2 where n 1 2 . References for Chapter 18 Abramowitz M. and Stegun I. A. Editors Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables National Bureau of Standards Applied Mathematics Washington . 1964. Bateman H. and Erdelyi A. Higher Transcendental Functions Vol. 1 and Vol. 2 McGraw-Hill New York 1953. Bateman H. and Erdelyi A. Higher Transcendental Functions Vol. 3 McGraw-Hill New York 1955. Gradshteyn I. S. and Ryzhik I. M. Tables of Integrals Series and Products Academic Press New York 1980. Magnus W. Oberhettinger F. and Soni R. P. Formulas and Theorems for the Special Functions of Mathematical Physics 3rd Edition Springer-Verlag Berlin 1966. McLachlan N. W. Bessel Functions for Engineers Clarendon Press Oxford 1955. Polyanin A. D. and Zaitsev V. F. Handbook of Exact Solutions for Ordinary Differential Equations 2nd Edition Chapman Hall CRC Press Boca Raton 2003. Slavyanov S. Yu. and Lay W. Special Functions A Unified Theory Based on Singularities Oxford University Press Oxford 2000. Weisstein E. W. CRC Concise Encyclopedia of Mathematics 2nd Edition CRC Press Boca Raton 2003. Zwillinger D. CRC Standard Mathematical Tables and Formulae 31st Edition CRC Press Boca Raton 2002. Chapter 19 Calculus of .