Look at notes for first lectures in other courses
... and a_1,...,a_d be complex constants with a_d non-zero. Suppose f:Z->C is a function satisfying f(n+d) + a_1 f(n+d-1) + ... + a_d f(n) = 0 for ALL n in Z. Then F(x) = sum_{n \geq 0)} f(n) x^n and G(x) = sum_{n > 0} f(-n) x^n are both rational functions and satisfy G(x) = – F(1/x). Example 1: f(n) = ...
... and a_1,...,a_d be complex constants with a_d non-zero. Suppose f:Z->C is a function satisfying f(n+d) + a_1 f(n+d-1) + ... + a_d f(n) = 0 for ALL n in Z. Then F(x) = sum_{n \geq 0)} f(n) x^n and G(x) = sum_{n > 0} f(-n) x^n are both rational functions and satisfy G(x) = – F(1/x). Example 1: f(n) = ...
Look at notes for first lectures in other courses
... Another look at paths through the digraph (thanks to Gregg): Put M = [[1,1],[1,0]] Look at the matrix sum_{n=0}^{infinity} M^n x^n, its entries are formal power series in x, and if you add them up, you get the generating function for paths from the left to the right. But we could also view this infi ...
... Another look at paths through the digraph (thanks to Gregg): Put M = [[1,1],[1,0]] Look at the matrix sum_{n=0}^{infinity} M^n x^n, its entries are formal power series in x, and if you add them up, you get the generating function for paths from the left to the right. But we could also view this infi ...
Algebra IB Name Final Review Packet #1 Chapter 8: Powers
... Some examples of trinomials are - ______________________________________________________________ The degree of a monomial is the _________________________________________________________________ To find the degree of a polynomial, find the ____________________________________. The __________________ ...
... Some examples of trinomials are - ______________________________________________________________ The degree of a monomial is the _________________________________________________________________ To find the degree of a polynomial, find the ____________________________________. The __________________ ...
Polynomials (Chapter 4) - Core 1 Revision 1. The polynomial p(x
... The polynomials f(x) and g(x) are defined by f(x) = x3 + px2 – x + 5 g(x) = x3 – x2 + px +1 where p is a constant. When f(x) and g(x) are divided by x – 2, the remainder is R in each case. Find the values of p and R (Total 5 marks) ...
... The polynomials f(x) and g(x) are defined by f(x) = x3 + px2 – x + 5 g(x) = x3 – x2 + px +1 where p is a constant. When f(x) and g(x) are divided by x – 2, the remainder is R in each case. Find the values of p and R (Total 5 marks) ...