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Chapter 11: Q12.3P (page 558)

Computer plot graphs of K(k) and E(k)in (12.3)for k = 0 - 1. Also plot 3Dgraphs of F(蠒,k)and E(蠒,k) in (12.1) for k = 0-1and蠒from 0-蟺2 and also from0-2蟺. Warning: Be sure you understand the notation used by your computer program; see text discussion just after (12.3) and Example 1.

Short Answer

Expert verified

Thegraphsare shown below.

Graph of K(k)

Graph of E(k)

Step by step solution

01

Given Information

The graphs are K(k), E(k)..

02

Definition of elliptic form.

The elliptic form of the integral is defined as F(蟺2,k)=鈭�0蟺211-k2sin2胃d胃.

03

Plot the graph of K.

The formula states that Kk=鈭�0蟺211-k2sin2胃d胃.

The graph is shown below.

04

Step 4:Plot the graph of E.

The formula states that Ek=鈭�0蟺211-k2sin2胃d胃.

The graph is shown below.

Hence the graph has been plotted.

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Most popular questions from this chapter

In Chapter 1, equations (13.5) and (13.6), we defined the binomial coefficientspnwhereis a non-negative integer butmay be negative or fractional. Show thatpn can be written in terms of螕functions as

role="math" localid="1664340642097" (pn)=螕p+1n!螕(p-n+1)

Express the following integrals as 尾 functions, and then, by (7.1) , in terms of 螕 functions. When possible, use 螕function formulas to write an exact answer in terms of 蟺,2 , etc. Compare your answers with computer results and reconcile any discrepancies.

role="math" localid="1664349717981" 鈭�01x41-x2dx

The integral (3.1) is improper because of infinite upper limit and it is also improper for 0 < p < 1 because xp-1becomes infinite at the lower limit. However, the integral is convergent for any p>0. Prove this.

Prove equation (6.5).

En(x)=鈭�1鈭�e-xttndt,n=0,1,2,....,andEi(x)=鈭�-鈭�tettdtand other similar

integrals are called exponential integrals. By making appropriate changes of variable, show that

  1. E1(x)=鈭�x鈭�e-ttdt
  2. role="math" localid="1664368570398" width="142" height="67">Ei(x)=-鈭�-x鈭�e-ttdt
  3. Ei(x)=-Ei(-x)
  4. 鈭�0xe1ttdt=E1(-1/x)

(Caution:Various notations are used; check carefully the notation in references you

are using.)
See all solutions

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