polynomials multiplying monomial binomial binomial 001

Ngày tải lên: 05/10/2016, 17:15

Ngày tải lên: 05/10/2016, 17:15

Ngày tải lên: 05/10/2016, 17:14

... CHAPTER The Binomial Distribution 1 1 1 6 10 15 10 20 15 Each number in the triangle is the sum of the number above and to the right of it and the number above and to the left of it For example, the ... number 10 in the fifth row is found by adding the and in the fourth row The number 15 in the sixth row is found by adding the and 10 in the previous row The...

Ngày tải lên: 24/10/2013, 08:20

... indicates the specific node in the final column of nodes 77 The Binomial Model (D) Assume the derivative depends only on the final stock price Corresponding to the stock price at each final node, there ... drops by the amount of the dividend Unfortunately, this dislocates the entire tree as shown The tree is said to have become bushy Let us recall the original random wal...

Ngày tải lên: 25/10/2013, 19:20

... [50] Develop computer programs for simplifying sums that involve binomial coefficients Exercise 1.2.6.63 in The Art of Computer Programming, Volume 1: Fundamental Algorithms by Donald ... beforehand Let’s give the floor to Dave Bressoud [Bres93]: The existence of the computer is giving impetus to the discovery of algorithms that generate proof...

Ngày tải lên: 20/12/2013, 19:15

... a bit on the preparation of the beholder A proof which is not understood will not produce the aha! reaction Of the proofs given for the binomial theorem the induction proof and the proof using ... proof of the Pythagorean Theorem) and others by the element of surprise in how their pieces fit together (Euclid’s proof of the Pythagorean Theorem) In this pape...

Ngày tải lên: 16/03/2014, 18:20

... terms of each binomial is Denote by xp the g.c.d of the first term of fu and the first term of fv , by xt the g.c.d of the first term of fu and the second term of fv , by xr the g.c.d of the second ... codimension Proof Since the Rees ring R(I) = K[x, T ]/J is of dimension n + 1, then Symmetric and Rees Algebras of Some Binomial Ideals 67...

Ngày tải lên: 06/08/2014, 05:20

... integer ≥ The idea of his proof was to compare the actual asymptotic behavior of the given sum, for fixed s and n → ∞, with the asymptotic behavior of a hypothetical closed form, and to show that the ... Recurrences for sums of powers of binomial coefficients, J Comb Theory Ser A 52 (1989), 77–83 [McI] Richard J McIntosh, Recurrences for alternating sums of powers of...

Ngày tải lên: 07/08/2014, 06:22

...  A BINOMIAL COEFFICIENT IDENTITY ASSOCIATED TO A CONJECTURE OF BEUKERS Scott Ahlgren, Shalosh B Ekhad, Ken Ono and Doron Zeilberger 

 Using the WZ method, a binomial coefficient identity ... sum satisfies a certain (homog.) third order linear recurrence equation To find the recurrence, and its proof, download the Maple package EKHAD and the Maple program ze...

Ngày tải lên: 07/08/2014, 06:22

... the q-binomial theorem and Theorems 1.2 and 1.3 Our combinatorial proof of the q-binomial theorem is based on Theorem 2.1, and is essentially the same as that of Alladi [2] or Pak [8] Proof of Theorem ... on the right-hand side is equal to q |µ| aodd(µ) µ∈P1 (µ)≤n The proof then follows from the involution σ in the proof of Theorem 2.1 Proof of Theorem 1.2 Replacing q a...

Ngày tải lên: 07/08/2014, 07:21

... Ekhad - K Ono - D Zeilberger, A binomial coefficient identity associated to a conjecture of Beukers, The Electronic J Combinatorics (1998), #R10 [3] F Beukers, Another congruence for Ap´ry numbers, ... Recently, Ahlgren and Ono [1] have shown that this conjecture is implied by the following beautiful binomial identity n n k k=1 2 n+k k + 2kHn+k + 2kHn−k − 4kHk = (1) which has...

Ngày tải lên: 07/08/2014, 08:20

... (3) and (4) are obviously equivalent Recently, an elegant combinatorial proof of (4) was given by Shattuck [12], and a little complicated combinatorial proof of (2) was provided by Chen and Pang ... combinatorial proofs for q = 1, we propose a combinatorial proof of (5) within the framework of partition theory by applying an algorithm due to Zeilberger [3] the electronic jou...

Ngày tải lên: 08/08/2014, 11:20

... version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version We also prove three somewhat unusual summation formulae, and use these to ... n=0 the electronic journal of combinatorics 18 (2011), #P60 (4.3) and (4.2) will then follow from the Identity Theorem, by an argument similar to that used in the proof...

Ngày tải lên: 08/08/2014, 14:22

... purpose of this paper is to give a q-analogue of (1.6) and (1.7) as follows: ⌊n/2⌋ k=0 ⌊n/4⌋ k=0 m+k k m+k k q2 n−2k m+n m+1 , q( ) = n n − 2k q q q4 n−4k m+1 q( ) = n − 4k q where the q -binomial coefficient ... k < We shall give two proofs of (1.8) and (1.9) One is combinatorial and the other algebraic the electronic journal of combinatorics 18 (2011), #P78 2 Bijective proof of...

Ngày tải lên: 08/08/2014, 14:23