INTEGRALS AND SERIES VOLUME 2 SPECIAL FUNCTIONS

科研必备数学工具书 Table Of Integrals, Series And Products 第七版

The question of the most expedient order in which to give the formulas, in particular, in what division to include particular formulas such as the definite integrals, turned out to be quite complicated. The thought naturally occurs to set up an order analogous to that of a dictionary. However, it is almost impossible to create such a system for the formulas of integral calculus. Indeed, in an arbitrary formula of the form

The preparation of the fourth edition of this handbook provided the opportunity to enlarge the sections on special functions and orthogonal polynomials, as suggested by many users of the third edition. A number of substantial additions have also been made elsewhere, like the enhancement of the description of spherical harmonics, but a major change is the inclusion of a completely new chapter on conformal mapping. Some minor changes that have been made are correcting of a few typographical errors and rearranging the last four chapters of the third edition into a more convenient form. A significant development that occurred during the later stages of preparation of this fourth edition was that my friend and colleague 英文原版超清

6th edition Table of Integrals_ Series and Products

Introduction 1 0.1 Finite Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.11 Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.12 Sums of powers of natural numbers . . . . . . . . . . . . . . . . . . . . . . . . 1 0.13 Sums of reciprocals of natural numbers . . . . . . . . . . . . . . . . . . . . . . 3 0.14 Sums of products of reciprocals of natural numbers . . . . . . . . . . . . . . . 3 0.15 Sums of the binomial coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.2 Numerical Series and Infinite Products . . . . . . . . . . . . . . . . . . . . . . 6 0.21 The convergence of numerical series . . . . . . . . . . . . . . . . . . . . . . . 6 0.22 Convergence tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 0.23–0.24 Examples of numerical series . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0.25 Infinite products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 0.26 Examples of infinite products . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 0.3 Functional Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 0.30 Definitions and theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Table of Integrals, Series, and Products (Eighth Edition) 数学积分微分工具书第七版

工科必备，最实用的、最全面的傅里叶积分闭式解

Elliptici 使用所描述的算术 - 几何平均数的方法来确定第一类、第二类不完全椭圆积分和雅可比 Zeta 函数的值。 实现的公式是 F(u,m) = int(1/sqrt(1-m*sin(t)^2), t=0..u); E(u,m) = int(sqrt(1-m*sin(t)^2), t=0..u); Z(u,m) = E(u,m) - E(m)/K(m)*F(u,m) 例程 Elliptici 适用于多维数组和任何范围的 u。 项目主页： http : //code.google.com/p/elliptic/

数学类，涵盖了各种常用定积分，不定积分，序列和乘法