User Argon

247 votes

4 answers

26k views

The Integral that Stumped Feynman?

asked Dec 8, 2012 at 18:24

122 votes

5 answers

9k views

Help find hard integrals that evaluate to $59$?

integration definite-integrals indefinite-integrals recreational-mathematics puzzle

asked Jul 9, 2012 at 3:02

74 votes

8 answers

11k views

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

real-analysis integration trigonometry

asked Aug 28, 2012 at 2:35

70 votes

9 answers

14k views

Do "Parabolic Trigonometric Functions" exist?

trigonometry conic-sections parametric

asked Apr 21, 2012 at 18:38

68 votes

6 answers

5k views

Am I too young to learn more advanced math and get a teacher?

soft-question advice learning

asked Jul 6, 2012 at 1:23

56 votes

12 answers

6k views

What is the fastest/most efficient algorithm for estimating Euler's Constant $\gamma$?

sequences-and-series limits numerical-methods estimation euler-mascheroni-constant

asked Apr 9, 2012 at 20:36

51 votes

4 answers

4k views

Proving $\sum_{n=-\infty}^\infty e^{-\pi n^2} = \frac{\sqrt[4] \pi}{\Gamma\left(\frac 3 4\right)}$

sequences-and-series complex-analysis integration summation contour-integration

asked Jul 3, 2013 at 0:25

40 votes

1 answer

5k views

How to choose a proper contour for a contour integral?

calculus integration complex-analysis contour-integration complex-integration

asked Mar 26, 2012 at 1:06

39 votes

4 answers

4k views

Good book on evaluating difficult definite integrals (without elementary antiderivatives)?

integration reference-request definite-integrals improper-integrals book-recommendation

asked Jul 27, 2012 at 23:45

36 votes

4 answers

11k views

How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$

limits fibonacci-numbers golden-ratio

asked Apr 15, 2012 at 23:23

35 votes

3 answers

31k views

Use of determinants

linear-algebra matrices self-learning determinant

asked Apr 4, 2012 at 2:16

31 votes

5 answers

7k views

Are there ways of finding the $n$-th derivative of a function without computing the $(n-1)$-th derivative?

calculus derivatives

asked May 3, 2012 at 1:26

31 votes

3 answers

2k views

Evaluating the integral $\int_{-\infty}^\infty \frac {dx}{\cos x + \cosh x}$

integration definite-integrals improper-integrals contour-integration

asked Feb 6, 2013 at 3:17

29 votes

5 answers

2k views

Evaluation of $\sum\limits_{n=0}^\infty \left(\operatorname{Si}(n)-\frac{\pi}{2}\right)$?

sequences-and-series integration special-functions analytic-number-theory

asked Aug 18, 2012 at 20:25

23 votes

1 answer

792 views

Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$

sequences-and-series complex-analysis theta-functions

asked Apr 1, 2014 at 1:04

22 votes

5 answers

4k views

How does partial fraction decomposition avoid division by zero?

linear-algebra algebra-precalculus integration partial-fractions

asked Jul 1, 2012 at 0:58

22 votes

4 answers

33k views

How to find the parametric equation of a cycloid?

geometry plane-curves

asked Apr 18, 2012 at 19:49

21 votes

1 answer

8k views

Evaluation of $\sum_{x=0}^\infty e^{-x^2}$

sequences-and-series integration special-functions closed-form

asked Jul 25, 2012 at 2:05

19 votes

3 answers

526 views

What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$

sequences-and-series complex-analysis quadratics

asked Jun 21, 2012 at 16:29

17 votes

1 answer

711 views

Closed form for $\sum_{n=2}^\infty \frac{1}{n^2\log n}$

integration sequences-and-series closed-form riemann-zeta

asked Dec 14, 2012 at 16:13

16 votes

2 answers

1k views

Sum with binomial coefficients and a square root

sequences-and-series binomial-coefficients summation

asked Apr 21, 2013 at 14:19

15 votes

2 answers

6k views

Has Euler's Constant $\gamma$ been proven to be irrational?

proof-writing irrational-numbers euler-mascheroni-constant

asked May 20, 2012 at 19:34

15 votes

3 answers

15k views

How to figure of the Laplace transform for $\log x$?

integration logarithms transformation laplace-transform

asked Apr 29, 2012 at 15:18

13 votes

2 answers

4k views

How was Euler able to create an infinite product for sinc by using its roots?

sequences-and-series trigonometry polynomials roots products

asked Apr 21, 2012 at 17:05

13 votes

3 answers

343 views

Evaluating a slow sum

calculus sequences-and-series definite-integrals

asked Mar 13, 2013 at 18:35

12 votes

1 answer

410 views

Why is $10\frac{\exp(\pi)-\log 3}{\log 2}$ almost an integer?

logarithms approximation pi

asked May 18, 2012 at 1:15

11 votes

2 answers

6k views

How do we know Taylor's Series works with complex numbers?

sequences-and-series complex-analysis trigonometry taylor-expansion

asked Jul 13, 2012 at 15:18

11 votes

2 answers

925 views

Derivative of $x^{x^{\cdot^{\cdot}}}$?

derivatives exponentiation tetration

asked Apr 29, 2012 at 17:50

11 votes

4 answers

9k views

Complex Analysis Solution to the Basel Problem ($\sum_{k=1}^\infty \frac{1}{k^2}$) [duplicate]

sequences-and-series complex-analysis complex-numbers pi

asked Apr 11, 2012 at 23:39

11 votes

1 answer

814 views

Evaluation of an integral involving the Lambert W function

integration special-functions definite-integrals lambert-w

asked Jan 5, 2013 at 23:16

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61 Questions

The Integral that Stumped Feynman?

Help find hard integrals that evaluate to $59$?

Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

Do "Parabolic Trigonometric Functions" exist?

Am I too young to learn more advanced math and get a teacher?

What is the fastest/most efficient algorithm for estimating Euler's Constant $\gamma$?

Proving $\sum_{n=-\infty}^\infty e^{-\pi n^2} = \frac{\sqrt[4] \pi}{\Gamma\left(\frac 3 4\right)}$

How to choose a proper contour for a contour integral?

Good book on evaluating difficult definite integrals (without elementary antiderivatives)?

How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$

Use of determinants

Are there ways of finding the $n$-th derivative of a function without computing the $(n-1)$-th derivative?

Evaluating the integral $\int_{-\infty}^\infty \frac {dx}{\cos x + \cosh x}$

Evaluation of $\sum\limits_{n=0}^\infty \left(\operatorname{Si}(n)-\frac{\pi}{2}\right)$?

Proving $\left(\sum_{n=-\infty}^\infty q^{n^2} \right)^2 = \sum_{n=-\infty}^\infty \frac{1}{\cos(n \pi \tau)}$

How does partial fraction decomposition avoid division by zero?

How to find the parametric equation of a cycloid?

Evaluation of $\sum_{x=0}^\infty e^{-x^2}$

What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$

Closed form for $\sum_{n=2}^\infty \frac{1}{n^2\log n}$

Sum with binomial coefficients and a square root

Has Euler's Constant $\gamma$ been proven to be irrational?

How to figure of the Laplace transform for $\log x$?

How was Euler able to create an infinite product for sinc by using its roots?

Evaluating a slow sum

Why is $10\frac{\exp(\pi)-\log 3}{\log 2}$ almost an integer?

How do we know Taylor's Series works with complex numbers?

Derivative of $x^{x^{\cdot^{\cdot}}}$?

Complex Analysis Solution to the Basel Problem ($\sum_{k=1}^\infty \frac{1}{k^2}$) [duplicate]

Evaluation of an integral involving the Lambert W function