Help me number 10.48, please do it step by steo. And make sure the words and symbols you use that i can understand 10.37. Show that(a) 1 = Jo(x) + 2J2 (x) + 2J4 (x) +...(b) J, (x) – J3(x) + J5(x) – J,(x) + •..10.38. Show that J1 (x)J2 (x) – 2J4 (x) + 3J6 (x) -•..T/22Jolm) = S10.39. Show thatcos (x sin e) do.T/21 - cos x10.40. Show that(a)cos 8) do =J, (x)T/2(b)| Jo(ar sin e) cos e sin e de0010.41. Show that| Jo(t) dt = 2 2 Jzx + 1 (x).k=000110.42. Show thate-azJ, (bx) dx =and thus firVa? + 62(a) L {J,(bt)},(b) L {J, (bt)}, (c) L(с)S.| J, (x) dx = 1.10.43. Show that10.44. Prove that |J,(x) <1 for all integers n.Is the resultBESSEL FUNCTIONS OF THE SECOND KIND10.45. Show that (a) Yn+1 (x)= 2" Y (x) – Yn-1(x), (b) Y10.46. Explain why the recurrence formulas for In(x) on page10.47. Prove that Y(x) = -Y,(x).10.48. Evaluate(a) Y1/2 (x), (6) Y_1/2(x).10.49. Prove that J, (x) Y (x) - J(x) Y, (x)= 2/Tx.(a) J 2*Y,(x) dz, (b) J r,(=) de,(6) J Y3 (x) dx, (c)10.50. Évaluate10.51. Prove the result (11), page 225.FUNCTIONS RELATED TO BESSEL FUNCTIONSx2x4+2210.52. Show thatI,(x)= 1 +2242+22426210.53. Show that(a) I„(x) = {In-1 (x) + In+1 (x)}, (b) xI,0010.54. Show thate(x/2)(t+1/t)is the generatin:- 00T/2210.55. Show thatI,(x)cosh (x sin e) de.10.56. Show that(a) sinh x= 2[1,(x) + 13(x) +• · ·](b) сosh x1,(x) + 2[1,(х) + l,(x) + ..].

Name: Help me number 10.48, please do it step by steo. And make sure the wor
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Help me number 10.48, please do it step by steo. And make sure the words and symbols you use that i can understand 10.37. Show that(a) 1 = Jo(x) + 2J2 (x) + 2J4 (x) +...(b) J, (x) – J3(x) + J5(x) – J,(x) + •..10.38. Show that J1 (x)J2 (x) – 2J4 (x) +