2. The gamma function generalizes the factorial, and is defined by T(x) = √°² t=² 0 tx-¹e-¹ dt, x> 0. It is known that for integer numbers, the function has the value T(n) = (n − 1)! = 1 · 2 · 3 · · (n − 1). (We furthermore define 0! = 1.) Consider using the data points (1, 1), (2, 1), (3, 2), (4, 6), (5, 24) to obtain interpolants that approximate l'(x). Using MATLAB, write a script that computes the polynomial interpolant of de- gree 4 for the above data points, and also a cubic spline interpolant (you may use the spline command in MATLAB, whose default end-conditions are 'not-a-knot'). Plot these two interpolants, and I'(x), on the interval [1, 5] in the same graph. Use a legend to label the functions. Note: (i) In MATLAB, the gamma function is produced using gamma. (ii) You don't have to find the explicit polynomial and spline formulas. Only the code and plot needs to be turned in.
2. The gamma function generalizes the factorial, and is defined by T(x) = √°² t=² 0 tx-¹e-¹ dt, x> 0. It is known that for integer numbers, the function has the value T(n) = (n − 1)! = 1 · 2 · 3 · · (n − 1). (We furthermore define 0! = 1.) Consider using the data points (1, 1), (2, 1), (3, 2), (4, 6), (5, 24) to obtain interpolants that approximate l'(x). Using MATLAB, write a script that computes the polynomial interpolant of de- gree 4 for the above data points, and also a cubic spline interpolant (you may use the spline command in MATLAB, whose default end-conditions are 'not-a-knot'). Plot these two interpolants, and I'(x), on the interval [1, 5] in the same graph. Use a legend to label the functions. Note: (i) In MATLAB, the gamma function is produced using gamma. (ii) You don't have to find the explicit polynomial and spline formulas. Only the code and plot needs to be turned in.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![2. The gamma function generalizes the factorial, and is defined by
T(x) = ²*
[²t²-¹e¹dt, x > 0.
0
It is known that for integer numbers, the function has the value
T(n) = (n − 1)! = 1 · 2 · 3 · · · (n − 1).
-
(We furthermore define 0! = 1.) Consider using the data points
(1, 1), (2, 1), (3, 2), (4, 6), (5, 24)
to obtain interpolants that approximate l'(x).
Using MATLAB, write a script that computes the polynomial interpolant of de-
gree 4 for the above data points, and also a cubic spline interpolant (you may use
the spline command in MATLAB, whose default end-conditions are 'not-a-knot').
Plot these two interpolants, and I'(x), on the interval [1, 5] in the same graph. Use a
legend to label the functions.
Note: (i) In MATLAB, the gamma function is produced using gamma. (ii) You don't
have to find the explicit polynomial and spline formulas. Only the code and plot
needs to be turned in.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F75e02168-4c21-4d2d-9b7a-15e2e8888347%2F8d74468f-9e3e-423d-84f9-6d081ab70ee8%2Fr8tpyer_processed.png&w=3840&q=75)
Transcribed Image Text:2. The gamma function generalizes the factorial, and is defined by
T(x) = ²*
[²t²-¹e¹dt, x > 0.
0
It is known that for integer numbers, the function has the value
T(n) = (n − 1)! = 1 · 2 · 3 · · · (n − 1).
-
(We furthermore define 0! = 1.) Consider using the data points
(1, 1), (2, 1), (3, 2), (4, 6), (5, 24)
to obtain interpolants that approximate l'(x).
Using MATLAB, write a script that computes the polynomial interpolant of de-
gree 4 for the above data points, and also a cubic spline interpolant (you may use
the spline command in MATLAB, whose default end-conditions are 'not-a-knot').
Plot these two interpolants, and I'(x), on the interval [1, 5] in the same graph. Use a
legend to label the functions.
Note: (i) In MATLAB, the gamma function is produced using gamma. (ii) You don't
have to find the explicit polynomial and spline formulas. Only the code and plot
needs to be turned in.
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