2. The gamma function generalizes the factorial, and is defined by r∞ T(x) = √² +² tx-¹e-t 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 Ã'(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 r∞ T(x) = √² +² tx-¹e-t 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 Ã'(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.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

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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