Explanation Given: The equations, J 1 / 2 ( x ) = 2 π x sin x , J − 1 / 2 ( x ) = 2 π x cos x , express J 3 / 2 ( x ) and J − 3 / 2 ( x ) in closed from. Approach: The property of Bessel function of the first kind, J p + 1 ( x ) = 2 p x J p ( x ) − J p − 1 ( x ) … ( 1 ) The formulas used are: J 1 / 2 ( x ) = 2 π x sin x , and J − 1 / 2 ( x ) = 2 π x cos x . Calculation: Substitute 1 2 for p in the equation ( 1 ) , that is, J 3 / 2 ( x ) = 1 x J 1 / 2 ( x ) − J − 1 / 2 ( x ) … ( 2 ) Substitute 2 π x sin x for J 1 / 2 ( x ) , and 2 π x cos x for J − 1 / 2 ( x ) in the equation ( 2 ) , J 3 / 2 ( x ) = 1 x 2 π x sin x − 2 π x cos x = 2 π x [ sin x − x cos x x ] = x − 3 2 2 π ( sin x − x cos x ) Thus, J 3 / 2 ( x ) = x − 3 2 2 π ( sin x − x cos x ) Substitute − 1 2 for p in the equation ( 1 ) and solve for J − 3 / 2 ( x ) ,

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ISBN: 9780321990167

Author: ANNIN

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 11.6, Problem 10P

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That all half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of sinx, cosx, and powers of x.

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Chapter 11.6, Problem 9P

Chapter 11.6, Problem 11P

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Chapter 11 Solutions

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That all half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of sin x , cos x , and powers of x .

Solution Summary: The author explains that half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of mathrmsinx, and

Videos

To show:

That all half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of sinx, cosx, and powers of x.

Want to see the full answer?

Chapter 11 Solutions

That all half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of sin x , cos x , and powers of x .

Solution Summary: The author explains that half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of mathrmsinx, and

Videos

To show: That all half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of sinx, cosx, and powers of x.

Want to see the full answer?

Chapter 11 Solutions

To show:

That all half-integer order Bessel functions of the first kind can be expressed as a finite sum of terms involving products of sinx, cosx, and powers of x.