Skip to main content
hasExams's user avatar
hasExams's user avatar
hasExams's user avatar
hasExams
  • Member for 12 years
  • Last seen more than 10 years ago
77 votes
5 answers
129k views

What exactly is Laplace transform?

11 votes
4 answers
13k views

Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$

11 votes
2 answers
2k views

how to prove $\displaystyle \frac{\sin (2n+1)\theta}{\sin \theta} = .... $

8 votes
2 answers
369 views

How to evaluate $ \int_0^\infty {1 \over x^x}dx$ in terms of summation of series?

7 votes
0 answers
189 views

How to evaluate $\int_0^\infty {x \over 1 + x^5} \;dx $? [duplicate]

6 votes
2 answers
322 views

how to show that $\lim_{z \to 0}z^z$ does not exist?

6 votes
3 answers
23k views

building transformation matrix from spherical to cartesian coordinate system

6 votes
2 answers
3k views

condition for roots of quartic equation to be purely imaginary

6 votes
7 answers
4k views

How to show that linear map is invertible?

4 votes
1 answer
4k views

how to show a scalar product defined by trace of matrices is non-degenerate

4 votes
3 answers
348 views

Find $ \lim_{n \to \infty } z_n $ if $z_{n+1} = \frac{1}{2} \left( z_n + \frac{1}{z_n} \right) $ [closed]

4 votes
3 answers
644 views

proving $\csc^2 \left( \frac{\pi}{7}\right)+\csc^2 \left( \frac{2\pi}{7}\right)+\csc^2 \left( \frac{4\pi}{7}\right)=8$

4 votes
4 answers
194 views

condition for two complex number $a$ and $b$ to be $|a+b| = |a| + |b|$

4 votes
5 answers
2k views

Does $i^i$ and $i^{1\over e}$ have more than one root in $[0, 2 \pi]$

4 votes
2 answers
514 views

Integrate: $\int \frac{dx}{x \sqrt{(x+a) ^2- b^2}}$

4 votes
2 answers
354 views

Asymptotic expansion of a function $\frac{4}{\sqrt \pi} \int_0^\infty \frac{x^2}{1 + z^{-1} e^{x^2}}dx$

3 votes
2 answers
997 views

How to evaluate $ \int_{-\infty}^\infty {e^{ax} \over 1 +e^x } \; dx $ [duplicate]

3 votes
4 answers
260 views

How to show that $\sum\limits_{n=1}^\infty \exp(i\,nz)$ converges?

3 votes
4 answers
21k views

How to find the laplace transform of $ |\sin (t)| $?

3 votes
2 answers
223 views

what is the easiest way to represent $ \sqrt{1 + x} $ in series

3 votes
1 answer
2k views

How to show $\sum x^n (1-x)$ does not converge uniformly on $[0,1]$

2 votes
1 answer
6k views

what is dimension of orthogonal complement of a subspace of a vector space.

2 votes
1 answer
1k views

the product of diagonals of a regular polygon

2 votes
5 answers
16k views

how to change polar coordinate into cartesian coordinate using transformation matrix

2 votes
2 answers
230 views

Evaluating $\sum_{k=1}^n k^x$ [duplicate]

2 votes
4 answers
4k views

Evaluate the integral $\int_0^{2 \pi} {\cos^2 \theta \over a + b \cos \theta}\; d\theta$

2 votes
2 answers
61 views

expressing $\sum_{k=0}^\infty \sum_{m=0}^k a_k a_m t^{m+k}$ as power series of $t$, $\sum_{n=0}^{\infty}a_n t^n $

2 votes
1 answer
2k views

expression for Remainder in Taylor theorem for complex variables

2 votes
3 answers
203 views

showing $1 + z + z^2 + \dots $ uniformly converges to $\frac{1}{1-z}$ for $|z| < 1$

2 votes
1 answer
106 views

calculate the roots of $z = 1 + z^{1/2}$ using Lagrange expansion