Mathematical Foundation of Computer Science

DHARM 44 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE For example, Let an = 3n + 2, then 3n + 2 > 3n for n ≥ 0, therefore an ...

DHARM DISCRETE NUMERIC FUNCTIONS AND GENERATING FUNCTIONS 45 | bn | ≤ C | an | for n ≥ C 0 So we have the equality | 2n | ≤ C. | ...

DHARM 46 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE and assume the scale of relation is 1 – pz – qz^2. So we have an – p an–1 – ...

DHARM DISCRETE NUMERIC FUNCTIONS AND GENERATING FUNCTIONS 47 Example 2.27 Find the numeric function for the generating function ...

DHARM 48 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE If bn = knan, where k is any arbitrary constant then corresponding generat ...

DHARM DISCRETE NUMERIC FUNCTIONS AND GENERATING FUNCTIONS 49 Note that Generating function to the convolution of numeric functio ...

DHARM 50 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE = 2 .3 ....... (n + 1)/n! = (n + 1) Therefore we obtain the numeric functio ...

DHARM DISCRETE NUMERIC FUNCTIONS AND GENERATING FUNCTIONS 51 Differentiate w.r.t z 1.5/(1 – 5z)^2 = 0 + 5.1 + 2.5^2 z + 3.5^3 z^ ...

DHARM 52 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE But we formally extend its previous definition to negative arguments by usi ...

DHARM DISCRETE NUMERIC FUNCTIONS AND GENERATING FUNCTIONS 53 (ii) – 1 + 6 + 30 + ........................... (iii) 1 + 6 + 24 + ...

DHARM 54 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE (ii) //function of summation of n numbers using recursion int Sum2(int A[ ] ...

DHARM DISCRETE NUMERIC FUNCTIONS AND GENERATING FUNCTIONS 55 (vi) // a function for polynomial evaluation using Horner’s rule in ...

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RECURRENCE RELATIONS wITH CONSTANT COEFFICIENTS 3.1 Introduction................................................................ ...

3.1 INTRODUCTION In mathematics, we often refer a function in terms of itself. For example, the factorial function f(n) = n!, fo ...

DHARM RECURRENCE RELATIONS WITH CONSTANT COEFFICIENTS 59 together with the base conditions. The numeric function is also referre ...

DHARM 60 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE if, kth order LRRCC has fewer than k values of numeric function then numer ...

DHARM RECURRENCE RELATIONS WITH CONSTANT COEFFICIENTS 61 So equation (3.11) is called characteristic equation. If α 1 is one of ...

DHARM 62 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE After solving we obtain multiple roots – 3, – 3, – 3 and – 3. Therefore, th ...

DHARM RECURRENCE RELATIONS WITH CONSTANT COEFFICIENTS 63 Step 2 Substitute general form of the particular solution into differen ...