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Chapter 1: Q29P (page 1)

Using the definition (2.1) of show that the following familiar formulas hold.

Short Answer

Expert verified

By using the definition 2.1, it is showed that the following familiar formula hold.

Step by step solution

01

Definition 2.1 of analytic function.

A function is analytic (or regular or holomorphic or monogenic) in a region of the complex plane if it has a (unique) derivative at every point of the region. The statement is analytic at a point means that has a derivative at every point inside some small circle about .

The derivative of is defined (just as it is for a function of a real variable) by the equation,

Where; and .

02

Apply definition 2.1.

Given the function is:

By the definition 2.1,

Solve the function is as follows:

Here it is clear that the following function hold by using the definition 2.1.

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Most popular questions from this chapter

鈭�0usinxdx1-x2

Show that24-x=1+18xwith an error less than132for 0<x<1. Hint: Let x=4y , and use the theorem (14.4) .

Prove that an absolutely convergent series 鈭�m=1鈭�anis convergent. Hint: Putbn=an+|an|. Then theare nonnegative; we have|bn|鈮�2|an|andan=bn-|an|

xsinx

Test the following series for convergence.

5.鈭�n=2鈭�(鈭�1)nlnn
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