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Principles of Colloid and Surface Chemistry, Revised and Expanded, 3rd Edition by Raj Rajagopalan, Paul C. Hiemenz

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Appendix A

Examples of Expansions Encountered in This Book

1.  Inverse of (1 – x):

1/(1x)=1+x+x2+x3+

2.  Logarithm:

ln(1+x)=x(1/2)x2+(1/3)x3(1<x<+1)

3.  Binomial:

(1±x)n=1±nx+[n(n1)/2!]x2±[n(n1)(n2)/3!]x3+(x2<1)

4.  Taylor’s series for f(x) around x = x0:

f(x)=f(x0)+(xx0)f(x0)+[(xx0)2/2!]f(x0)+

where each prime on f indicates a differentiation with respect to x.

5.  Sine function:

sinx=xx3/3!+x5/5!

6.  Hyperbolic sine function:

sinhx=x+x3/3!+x5/5!+

7.  Hyperbolic cosine function:

cosh x=1+x2/2!+x4/4!+

8.  Exponential function:

ex=1+x+x2/2!+x3/3!+

REFERENCE

Gradshteyn, I. S., and Ryzhik, I. M., Table of Integrals, Series, and Products, 5th ed., Academic Press, New York, 1993. (There are numerous excellent reference books available ...

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