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Chapter 11: Q1P (page 543)
Prove that . Hint:Putin Equation (6.1).
The statement is proved.
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Without computer or tables, but just using facts you know, sketch a quick rough graph of the function from -2to 3. Hint:This is easy; don鈥檛 make a big job of it. From Section 3, you know the values of the data-custom-editor="chemistry" function at the positive integers in terms of factorials. From Problem 1, you can easily find and plot the function at , . (Approximateas a little less than 2.) From (4.1) and the discussion following it, you know that the function tends to plus or minus infinity at 0 and the negative integers, and you know the intervals where it is positive or negative. After sketching your graph, make a computer plot of the 螕 function from -5to 5and compare your sketch.
Prove that erf(x) is an odd function of x. Hint: Put t = -s in (9.1) .
Show that for integral n, m,
Hint: See Chapter 1, Section 13C, Problem 13.3.
In the pendulum problem, is an approximate solution when the amplitude 伪 is small enough for the motion to be considered simple harmonic. Show that the corresponding exact solution when 伪 is not small is is the modulus of the elliptic function. Show that this reduces to the simple harmonic motion solution for small amplitude 伪
Use Stirling鈥檚 formula to evaluate .
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