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Chapter 12: Q8-2P (page 562)

Find the norm of each of the following functions on the given interval and state the normalized function $P_{2} (x) on (- 1, 1)$

Short Answer

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Concept of normalization factor

Calculate the norm of the function

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Most popular questions from this chapter

Verify by direct substitution that the text solution of equation (16.3) and your solutions in the problems above are correct. Also prove in general that the solution (16.2) given for (16.1) is correct. Hint: These are exercises in partial differentiation. To verify the solution (16.4) of (16.3), we would change variables from x,y to say z, u where $y = x^{1 / 2} u, u = J_{1 / 3} (z), z = 2 x^{3 / 2}$ , and show that if x,y satisfy then u , z satisfy, $(z^{2} - \frac{1}{9}) u + z \frac{du}{dz} + z^{2} \frac{d^{2} u}{{dz}^{2}} = 0$ .

Prove the given system of equations $I_{1 / 2} (x) = \sqrt (\frac{2}{π (x)} s i n h (x)$ and $K_{1 / 2} (x) = \sqrt (\frac{π}{2 (x)} e^{(- x)} .$

Use L23of the Laplace Transform Table (page 469 ) to evaluate $\int_{0}^{\infty} {tJ}_{0} (2 t) e \hat{} - tdt$ .

Use the table above and the definitions in Section 17 to find approximate formulas for large x for $h_{n}^{(2)} (i x)$ :

To show the first few terms of $J_{0} (x), J_{1} (x), J_{- 1} (x), J_{2} (x), J_{- 2} (x)$ . Show that $J_{- 1} (x) = - J_{1} (x) {andJ}_{- 2} (x) = J_{2} (x)$ .

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Find the norm of each of the following functions on the given interval and state the normalized function $P_{2} (x) on (- 1, 1)$

Short Answer

Step by step solution

Concept of normalization factor

Calculate the norm of the function

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Find the norm of each of the following functions on the given interval and state the normalized functionP2(x)on(-1,1)

Short Answer

Step by step solution

Concept of normalization factor

Calculate the norm of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Electricity

Wave Optics

Fields in Physics

Fundamentals of Physics

Electrostatics

Study anywhere. Anytime. Across all devices.

Find the norm of each of the following functions on the given interval and state the normalized function $P_{2} (x) on (- 1, 1)$