Quiz. Let complex matrices. Suppose that
Prove or disprove the following proposition;
Problem. is a matrix which satisfies
Find all possible values of .
A continuous function satisfies the following equality;
Hint. AM-GM inequality
Problem. (제 29회 전국 대학생수학경시대회 제 2분야 8번)
Calculate where .
We first expand to Taylor series, and exchange the summation and integral;
We can calculate the integral using Gamma function; (I love this function 🙂 )
A few days ago, I bought the score of Sinfonietta(composed by N.Kapustin), which is one of my favorite music 🙂
새우깡 CF + Happy Things(by J Rabbit)
played by me
Prove that .
I saw this problem at http://sos440.tistory.com/34.
Substitute , then becomes
Now we use the following formula(which is one of my favorite formulas);
By this formula,
We can easily prove that ; For the second integral, we interchange summation and integral… then
Using basic trigonometric identities, we can prove that
A few days ago, I wrote an article about usefulness of Leibniz rule(it is sometimes called ‘differentiation under integral sign’) in calculating hard integrals. I submitted the article to the math club of my school; I’m still waiting for it to be accepted…
pdf file ; ML – Leibniz rule_2nd version (the article is written in Korean)