100÷9899=? (Introduction to Generating Functions & Formal Power Series) [English Subtitles]
Рет қаралды 13,800
Күн бұрынWe'll introduce generating functions and formal power series as simply and concisely as possible.
Almost no prior knowledge is required. You're good to go if you're comfortable with sigma notation.
0:00 100/9899
1:08 What are Generating Functions?
2:08 Generating Function of 0,1,4,9...
4:11 0+1+4+9+...
X: / evima0
@name-break 26 күн бұрын
私立高校入試とかでやけに綺麗な規則性のある分数を見つけたなあっていつも思ってたけど自分で作れるんだ
@user-hd2kc9le7y 4 ай бұрын
0,1,4,9の母関数を求めるあたりで、1/(1-x)^2を求めるときに1/(1-x)の両辺を形式微分してもいいかもですね
@evimalab 4 ай бұрын
不明点があればお気軽に質問してください。（母関数一般については詳しくありませんが…） If something was unclear, please feel free to ask. (I don't know much about generating functions in general, though...)
@11ex2pha686 4 ай бұрын
めちゃ面白い、良コンテンツ
@evimalab 4 ай бұрын
ありがとうございます！励みになります。
@khoitan4758 4 ай бұрын
Now I see why this is related to combinatorics. What a shock!
@256yayo 2 ай бұрын
nCkってchooseって読むんだ
@banboo0427 Ай бұрын
ChooseというよりはCombinationだと思われる
@ST-gs6ul Ай бұрын
英語圏では一般にnCkをn choose kと読むようです。 2 * 3 は正式には2 multiplied by 3ですが、口語的に2 times 3というようなものでしょうか。
@Ahryno781 4 ай бұрын
Is this discrete mathematics?
@evimalab 4 ай бұрын
I think so. Generating functions and formal power series are used extensively in combinatorics.
@p0utan 26 күн бұрын
Yes. And this idea is connected to analysis and develops into, for example, analytic number theory.
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