In this section, we see how can be used to derive another useful identity. We begin by establishing a different recursive formula for P(p,k) than was used in our definition of it.
An Application of the Binomial Theorem
In this section, we see how can be used to derive another useful identity. We begin by establishing a different recursive formula for \(P(p,k)\) than was used in our definition of it.
Our goal in this section will be to invoke with the exponent \(p=-1/2\). To do so in a meaningful manner, we need a simplified expression for \(C(-1/2,k)\), which the next lemma provides.
We will return to this generating function in , where it will play a role in a seemingly new counting problem that actually is a problem we've already studied in disguise.
Now recalling about the coefficients in the product of two generating functions, we are able to deduce the following corollary of by squaring the function \(f(x) = (1-4x)^{-1/2}\).
Indi sen
Hiç bir hasapçy buny çözmez, emma onuň bölekleri hasaplanmak üçindir. Aşakda birini synla ýa-da özüňi ýaz.
Özüň işle
Mugt hasap her bir ders üçin notlar goşýar, tamamlanan zadyňyzyň ýazgysyny, çözen problemaňyzy bir ýerde, we bu sahypa barada sorap biljek mugallymy. Matematika özüçe her kim üçin açyk, girseň ýa girmeseň.
Eň täze düşündirme, surat, we her harpyň manysy üçin her bir simwoly basyň.
Her bir bölegiň manysy
Resim
Bilen
Mysal
Bu beýanda hem ulanylan
Adamlar soraýan soraglar
Permutation or combination?
Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).
What is a graph in this sense?
Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.
Bu sahypanyň käbir bölegi şundan alyndy
Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0).
Bu ýerde gysgaldylan we tekrar beýan edilen; hatalar biziňkidir.