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.2 2! +... 4! 6!

.2 2! +... 4! 6!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the table in the picture to help you find a Function with the indicated series representation.

Table 11.5 1 =1 + x + x² + . ..+x* + r*, for |x| < 1 1 Iso = 1 – x + x² –..+ (-1)*x* - 1 + x + • (-1)*x, for x| < 1 for |x| < 1 k=0 x² e = 1 + x + 2! for x< ∞ %3D k! k! k=0 :). (-1)*x2k+1 (2k + 1)! (-1)*x²*+1 Σ k=0 (2k + 1)! it sin x = x - 3! for x < ∞ 5! (-1)* x24 x² x* k 2k (-1)* x* 2k 00 cos x = 1 for |x| < 0 %3D 2! 4! (2k)! (2k)! k=0 x² In (1 + x) = x (-1)*+1 xk + · . 3. (-1)*+1k for -1 < x < 1 k k=1 3. -In (1 – x) = x + 2, for -1 sx< 1 + . 3 k=1 k 2k+1 (-1)*x2k+1 (-1)* x²*+1 -1 tan'x = x Σ 2k + 1 for x < 1 %3D 3 2k + 1 k=0 5. 2k+1 x2k+1 sinh x = x+ 3! for x < ∞ 5! (2k+1)! k=0(2k + 1)!' 2k 2k x- cosh x = 1+ 2! Σ (2k)!" for x < ∞ 4! (2k)! *, for |x| < 1 and p(p - 1)(p- 2) (p – k+ 1) (0) (1 + x)' = %3D k! 8. 8. 8. 8. +. +.
Transcribed Image Text:Table 11.5 1 =1 + x + x² + . ..+x* + r*, for |x| < 1 1 Iso = 1 – x + x² –..+ (-1)*x* - 1 + x + • (-1)*x, for x| < 1 for |x| < 1 k=0 x² e = 1 + x + 2! for x< ∞ %3D k! k! k=0 :). (-1)*x2k+1 (2k + 1)! (-1)*x²*+1 Σ k=0 (2k + 1)! it sin x = x - 3! for x < ∞ 5! (-1)* x24 x² x* k 2k (-1)* x* 2k 00 cos x = 1 for |x| < 0 %3D 2! 4! (2k)! (2k)! k=0 x² In (1 + x) = x (-1)*+1 xk + · . 3. (-1)*+1k for -1 < x < 1 k k=1 3. -In (1 – x) = x + 2, for -1 sx< 1 + . 3 k=1 k 2k+1 (-1)*x2k+1 (-1)* x²*+1 -1 tan'x = x Σ 2k + 1 for x < 1 %3D 3 2k + 1 k=0 5. 2k+1 x2k+1 sinh x = x+ 3! for x < ∞ 5! (2k+1)! k=0(2k + 1)!' 2k 2k x- cosh x = 1+ 2! Σ (2k)!" for x < ∞ 4! (2k)! *, for |x| < 1 and p(p - 1)(p- 2) (p – k+ 1) (0) (1 + x)' = %3D k! 8. 8. 8. 8. +. +.
.2 2! +... 4! 6!
Transcribed Image Text:.2 2! +... 4! 6!
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