Mathlover

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2521

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I am an engineer who is in love with math and lifelong math student. I love to learn new things in mathematics for self-satisfaction. My idols are Gauss , Euler , Ramanujan because they were in love with math as I feel.

	2,920 reputation	bio	website		visits	member for	1 year, 4 months
2521 badges		location			seen	3 hours ago

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169 Favorites

added views newest activity votes

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157

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sum of infinite series

aug 28 at 20:57 Robert Israel 86.4k

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answer

133

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Combinatorial proof that $\sum_{k=0}^n \binom{n}{k} \frac{(-1)^k}{(k+1)^2} = \frac{H_{n+1}}{n+1}$

combinatorics binomial-coefficients

dec 12 at 18:37 Mike Spivey 25.9k

votes

answers

195

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Continuous solutions of $f(x) = \lambda \int_0^{\pi/2} \cos({x-y)}f(y)\,dy$

functional-analysis integral-equations

aug 24 at 14:00 Jayesh Badwaik 1,215

votes

answer

179

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prove equality with integral and series

homework integral integration special-functions approximation-theory

jun 17 '12 at 22:19 Norbert 20.6k

votes

answer

285

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Prove that Pascals triangle contains only natural numbers, using induction.

binomial-coefficients

jun 26 '12 at 22:51 Michael Hardy 48.3k

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124

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Show $\lim_{N\to \infty}\sum_{k=1}^{N}\frac{1}{k+N}=\ln(2)$

sequences-and-series limit

feb 16 at 12:04 Arjang 2,447

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answers

306

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Calculating $\frac{\partial^{1/2}}{\partial x^{1/2}}\left( e^{-\alpha x^2 + \beta x} \right) $

fractional-calculus

apr 25 at 12:59 Mhenni Benghorbal 14.2k

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answers

193

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Primitive roots of unity

real-analysis elementary-number-theory complex-numbers

apr 19 '12 at 20:46 Jyrki Lahtonen 30.9k

votes

answer

128

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When is the pushout of a monic also monic?

category-theory homological-algebra

jun 6 '12 at 8:25 Martin Brandenburg 22.9k

votes

answer

387

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An Identity Concerning the Riemann Zeta Function

number-theory analysis riemann-zeta

feb 15 '12 at 14:26 Neves 1,120

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109

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Evaluate $\frac{1}{2\pi}\int _{-\pi}^\pi \frac{e^{-i\varphi}}{1-k\cos (\varphi)} \, \mathrm{d}\varphi$

integral

mar 9 at 19:27 vonbrand 6,616

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answer

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Integration of $\displaystyle \int\frac{1}{1+x^8}dx$

calculus

2d ago Raskolnikov 6,975

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answer

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Geometric proof

geometry

may 16 at 7:15 user17762 76.4k

votes

answers

120

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A question about an equilateral triangle

geometry

mar 15 at 16:47 lab bhattacharjee 29k

votes

answer

109

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Prove that $\int_0^{\pi/2} \cos^{p+q-2}(\theta) \cos((p-q)\theta)d\theta = \frac{\pi}{(p+q-1)2^{p+q-1}B(p,q)}$

complex-analysis special-functions definite-integral

mar 3 at 12:44 Random Variable 1,691

votes

answers

154

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Need some hint or technique for this integral

calculus real-analysis sequences-and-series integral

mar 2 at 14:12 Sasha 41.4k

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answer

273

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how to calculate this infinite integral of infinite product of cosine

analysis integral

may 31 '12 at 15:43 GEdgar 19k

votes

answer

180

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How to prove Gauss's Digamma Theorem?

calculus number-theory special-functions

may 28 '12 at 20:45 M Turgeon 4,551

votes

answer

144

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About the remainder of Taylor expansion and Riemann-Liouville integral

analysis

jun 9 '12 at 5:34 Community♦ 1

votes

answers

135

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Which polynomial equations of higher degree will have a solution formula?

abstract-algebra group-theory polynomials problem-solving

mar 23 '12 at 21:26 Robert Israel 86.4k

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answers

265

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Evaluate $\lim_{x \to 0} \left(\frac{1}{\ln(1+x)} + \frac{1}{\ln(1-x)}\right)$

calculus limit

apr 16 '12 at 11:29 robjohn♦ 60k

votes

answer

123

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Showing a function satisfies a particular differential equation

complex-analysis differential-equations

may 20 '12 at 21:06 doraemonpaul 3,047

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answers

372

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Factorize polynomial over $GF(3)$

polynomials finite-fields factoring coding-theory

apr 14 '12 at 16:26 Lierre 2,882

votes

answers

202

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How to find generating function of cumulative sum?

number-theory generating-functions

apr 13 '12 at 6:40 Gerry Myerson 86k

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answers

746

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Visual Ways to Remember Cross products of Unit vectors? Cross-product in $\mathbb F^3$?

geometry cross-product

jan 13 at 6:10 hhh 1,500

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answers

kviews

How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?

geometry transformation 3d

jul 10 at 15:41 Matthew Slyman 6

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answer

416

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Convert Airy's equation, $y'' - xy = 0$, into Bessel equation, $t^2u'' + tu' + (t^2 - c^2)u = 0$

homework differential-equations

may 19 '12 at 21:48 doraemonpaul 3,047

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answer

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Property of sum $\sum_{k=1}^{+\infty}\frac{(2k+1)^{4n+1}}{1+\exp{((2k+1)\pi)}}$

sequences-and-series analysis special-functions

oct 19 at 7:47 Martin Sleziak 20.3k

votes

answers

169

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Transforming Differential Equation to a Kummer's Equation

differential-equations transformation hypergeometric-function

sep 4 at 1:33 doraemonpaul 3,047

votes

answers

119

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Minimum path cost

geometry

sep 21 at 5:03 Haider 31