Page 320 - Schaum's Outline of Differential Equations

CHAP. 30] GAMMA AND BESSEL FUNCTIONS 303

Supplementary Problems

30.19. FindT(2.6).

30.20. Findr(-1.4).

30.21. Findr(4.14).

30.22. FindT(-2.6).
30.23. Find r(-1.33).

30.24. Express as a gamma function.

30.25. Evaluate

30.26. Prove that

30.27. Prove that

Hint: Use Problem 30.11.
30.28. Prove that

30.29. (a) Prove that the derivative of

Hint: Use (1) of Problem 30.13 and (1) of Problem 30.14.

(b) Evaluate in terms of Bessel functions.

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30.30. Show that y = xJ n(x) is a solution of x y" - xy' + (1 + x - n )y = 0.
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30.31. Show that y = x J (x) is a solution of xy" - 3y' + xy = 0.
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