Handbook of Mathematics by I.N. Bronshtein, K.A. Semendyayev, Gerhard Musiol, Heiner

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By I.N. Bronshtein, K.A. Semendyayev, Gerhard Musiol, Heiner Mühlig

This advisor booklet to arithmetic includes in guide shape the elemental operating wisdom of arithmetic that is wanted as a daily consultant for operating scientists and engineers, in addition to for college students. effortless to appreciate, and handy to take advantage of, this consultant ebook supplies concisely the data essential to overview such a lot difficulties which happen in concrete functions. within the more moderen variants emphasis used to be laid on these fields of arithmetic that grew to become extra very important for the formula and modeling of technical and usual methods, specifically Numerical arithmetic, chance thought and information, in addition to details Processing. along with many improvements and new paragraphs, new sections on Geometric and Coordinate variations, Quaternions and functions, and Lie teams and Lie Algebras have been further for the 6th edition.

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I "J2k + I "52k + I 72k I ± -;;>k + ... + (2n - 1t2• 22•-1 + ... 1)2k "2'(22k-t _ + ... 1t2k(22k - 2 · (2k)! Euler numbers E, 22. I - I Jlk+l + I I s>k+l - 7lk+l + ... ± (2n _ 1)2k+1 1) B,, (2k)! + ... I) B •. 2 5 I 5 61 1385 50521' 2702765 199360981 6 7 Table of the power series expansions of some functions Function Power series expansion Interval of convergence Algebraic functions Binomial series By transforming am ( l ± : )m one is led to the following series: 1X,

Sec no. 241). dx -;jX (sec no. 246). (see no. 241). 3 256. 257. /e X 258. 259. I I I 5b2- 4ae 16a 2 2e 41 (see no. 248). I + cl (see no. 245). /X dx for c > 0, for c > 0, Ll > o. 11 for c < 0, Ll < 0. 3 Integrals and sums of series (see no. 258). (see nos. 241 and 258). (-see nos. 241 and 258). 262. 263. 264. 265. 266. j(2ax - x2) + I + fI dx X(2a-l)J2 +c I x<2n-l)/2 X dx (see nos. 245 and 260). - ..!..... /(ax2 + bx). bx x-a a = arcsin---. /(lax - x 2 ) x-a dx = - 2- x-a a + a arcsin---. /(lax - x 2) a2 +T x-a arcsin - a - .

Lnx. I x2 I + 2a4 X + (j6 1n x· I + I 4a4X 2 + a•x 3 x2 + '"2a8 1nx. [c In (b + ex) - c2 In X ± 1 dx = cz) X a 2 c 2 ± b2 ± 15 xz I 2a4 + a3 Y. + 8a6 X =F """8"d7 4a4 X 2 + I J + TaT x + = - 2a4x2 Integrals containing x· Y. i6ln + 2a4X + 1 dx x2 1 27 1nx. ba Y] . x3 Natation: X = a3 ± x3; in case a formula contains a double sign, the upper sign belongs to X = a 3 the lower one to X = a3 - x3. 83. I 84. I dx -;(" dx '"'X2 I = ± 6a21n a• = Ja3 X x (a ± x) 2 + ax + 2Idx 86. I xdx '"'X2 6a x2 = Ja3 X + (a ± x) 1 Ixdx 3aJ 1 2x + a + -;;>:j3 arctan -;;J3".

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