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Chapter 6: 6.4 41E (page 236)

Short Answer

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Step by step solution

01

Define Spherical Bessel’s equation.

Bessel functions of half-integral order are used to dene two more important functions:

02

Find the graph of J3/2(X)

Use GNU Octave to plot the functions.

03

Find the value of J-3/2(X)

Let,

04

Find the value of j5/2(X)

Let,

05

Find the value of j-5/2(X)

Let,

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Most popular questions from this chapter

Bessel’s Equation

In Problems 1-6 use (1) to find the general solution of the given differential equation on(0,∞).

2.

localid="1664866362361" x2y''+xy'+(x2-1)y=0

Is x=0an ordinary or a singular point of the differential equation xy''+(sinx)y=0? Defend your answer with sound mathematics. [Hint: Use the Maclaurin series ofand then examine(sinx)/x.]

In Problems 25-30 proceed as in Example 3 to rewrite the given expression using a single power series whose general term involves xk.

∑n=1∞nCnxn-1-∑n=0∞Cnxn

In Problems 15–24, x = 0is a regular singular point of the givendifferential equation. Show that the indicial roots of the singularity do not differ by an integer. Use the method of Frobenius to obtain two linearly independent series solutions about x= 0. Form the general solution on (0,∞).

x2y''-(x-29)y=0

Find the general solution of the given differential equation on0,∞

x2y''+x2-2yy=0
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