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) + ..].

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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) +

Answered: 10.48. Evaluate (a) Y1/2(x), (b)…

Math

Advanced Math

10.48. Evaluate (a) Y1/2(x), (b) Y-1/2(x).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 52E

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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/2
2
Jolm) = S
10.39. Show that
cos (x sin e) do.
T/2
1 - cos x
10.40. Show that
(a)
cos 8) do =
J, (x)
T/2
(b)
| Jo(ar sin e) cos e sin e de
00
10.41. Show that
| Jo(t) dt = 2 2 Jzx + 1 (x).
k=0
00
1
10.42. Show that
e-azJ, (bx) dx =
and thus fir
Va? + 62
(a) L {J,(bt)},
(b) L {J, (bt)}, (c) L
(с)
S.
| J, (x) dx = 1.
10.43. Show that
10.44. Prove that |J,(x) <1 for all integers n.
Is the result
BESSEL FUNCTIONS OF THE SECOND KIND
10.45. Show that (a) Yn+1 (x)
= 2" Y (x) – Yn-1(x), (b) Y
10.46. Explain why the recurrence formulas for In(x) on page
10.47. 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. Évaluate
10.51. Prove the result (11), page 225.
FUNCTIONS RELATED TO BESSEL FUNCTIONS
x2
x4
+
22
10.52. Show that
I,(x)
= 1 +
2242
+
224262
10.53. Show that
(a) I„(x) = {I
n-1 (x) + In+1 (x)}, (b) xI,
00
10.54. Show that
e(x/2)(t+1/t)
is the generatin:
- 00
T/2
2
10.55. Show that
I,(x)
cosh (x sin e) de.
10.56. Show that
(a) sinh x
= 2[1,(x) + 13(x) +
• · ·]
(b) сosh x
1,(x) + 2[1,(х) + l,(x) + ..].

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