User doraemonpaul

4

8

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1

answer

338

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About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$

indefinite-integrals

May 19 '14 at 23:42 Yiannis Galidakis 3,431

4

8

votes

1

answer

535

views

$\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$

laplace-transform contour-integration

Apr 9 '13 at 4:54 doraemonpaul 15k

2

8

votes

3

answers

2k

views

How to find the general solution of $xy''-(2x+1)y'+x^2y=0$ when we know the general solution of $y''+2y'+xy=0$?

ordinary-differential-equations

Feb 24 '13 at 0:24 Community♦ 1

3

6

votes

2

answers

558

views

Why solving $\dfrac{\partial u}{\partial x}=\dfrac{\partial^2u}{\partial y^2}$ like this is wrong?

partial-differential-equations fake-proofs

Jul 9 '12 at 4:08 Community♦ 1

1

5

votes

0

answers

316

views

How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

partial-differential-equations

Mar 31 '13 at 21:00 Community♦ 1

2

5

votes

1

answer

458

views

About fractional differentiation under the integral sign

fractional-calculus

Aug 3 '12 at 7:33 draks ... 17.7k

3

4

votes

1

answer

809

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About finding the general solution of first-order totally nonlinear PDE with two independent variables

partial-differential-equations

Jul 3 '17 at 10:31 Community♦ 1

4

votes

1

answer

1k

views

Is it possible for cosine functions to have Fourier sine series expressions or sine functions to have Fourier cosine series expressions?

fourier-series

Nov 29 '12 at 23:44 Micah 35.2k

4

votes

1

answer

229

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About differentiation under the product integral sign

calculus definite-integrals

Aug 1 '12 at 22:41 Henry T. Horton 16.8k

3

votes

0

answers

57

views

About the second-order linear ODEs with polynomial coefficients

ordinary-differential-equations

Nov 29 '15 at 19:14 doraemonpaul 15k

3

votes

3

answers

388

views

Longest cylinder of specified radius in a given cuboid

geometry

Jul 5 '15 at 4:18 Harish Chandra Rajpoot 35.8k

3

votes

0

answers

101

views

fancy about some properties of kernel functions at infinity

analysis definite-integrals integral-transforms

Apr 15 '13 at 4:51 doraemonpaul 15k

1

3

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1

answer

2k

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Does solve PDE by combination of variables always cannot find the general solutions?

partial-differential-equations

Apr 3 '13 at 13:49 Community♦ 1

1

3

votes

3

answers

148

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Iterations of $f(x)=\dfrac{ax+b}{cx+d}$

functional-equations function-and-relation-composition

Nov 19 '12 at 16:54 alex.jordan 49.5k

2

votes

1

answer

112

views

Properties about the Generalized Legendre-type polynomial sequence $f_n(x)=\frac{d^n}{dx^n}(p(x)^n)$

analysis ordinary-differential-equations orthogonal-polynomials

Apr 23 '14 at 15:03 rrogers 773

2

votes

0

answers

730

views

About the inverse laplace transform of sinc function

laplace-transform contour-integration

Apr 10 '13 at 3:58 doraemonpaul 15k

2

votes

0

answers

161

views

How to solve the PDEs with more than two independent variables whose their most-general solutions are known?

partial-differential-equations

Mar 31 '13 at 21:10 Community♦ 1

2

votes

1

answer

335

views

about discrete versions of “inverse laplace transform”

laplace-transform

Dec 3 '12 at 12:04 doraemonpaul 15k

1

2

votes

1

answer

628

views

fancy about inverse discrete Fourier sine and cosine transform (i.e. Fourier sine and cosine series)

fourier-analysis integral-transforms

Sep 23 '12 at 2:05 doraemonpaul 15k

1

vote

0

answers

42

views

About the linear PDE $u_{x_1x_2x_3…x_n}=u$

partial-differential-equations

Nov 17 '17 at 15:49 doraemonpaul 15k

1

vote

0

answers

65

views

How the change of variables of a PDE affects the given condition(s)?

partial-differential-equations

Mar 30 '14 at 0:38 Ellya 11k

1

vote

0

answers

101

views

How are the general skills for complete factorization of arbitrary homogeneous order polynomials in $\mathbb{C}$?

polynomials factoring

Mar 27 '14 at 22:21 doraemonpaul 15k

1

vote

0

answers

81

views

Properties about the Generalized Hermite-type polynomial sequence $f_n(x)=e^{-p(x)}\frac{d^n}{dx^n}e^{p(x)}$

analysis ordinary-differential-equations orthogonal-polynomials

Aug 12 '13 at 1:23 doraemonpaul 15k

1

vote

0

answers

72

views

Are there the resources mentioned about finding the general solutions of some first order fully nonlinear PDE examples by method of characteristics?

reference-request partial-differential-equations

Jan 24 '13 at 2:43 Community♦ 1

1

vote

1

answer

99

views

How to prove the periodicity of an iterated function?

periodic-functions function-and-relation-composition

Nov 20 '12 at 4:05 uncookedfalcon 4,012

1

vote

1

answer

378

views

Advanced improper integral involving periodic function of polynomial

calculus real-analysis improper-integrals

Nov 9 '12 at 5:37 Lukas Geyer 16.6k

1

vote

1

answer

477

views

How to compute the convolution of two functions which diverge at infinity?

convolution

Nov 1 '12 at 19:51 Robert Israel 405k

1

0

votes

2

answers

132

views

Does Heun's differential equation have other known types confluent approach?

ordinary-differential-equations

Nov 21 '18 at 17:45 Przemo 8,128

0

votes

2

answers

162

views

Evaluate $\sum\limits_{n=0}^\infty n^ke^{-an^2}$ and $\sum\limits_{n=0}^\infty(-1)^nn^ke^{-an^2}$ .

sequences-and-series special-functions theta-functions

Sep 7 '16 at 8:55 user90369 11.1k

1

0

votes

0

answers

131

views

About evaluating $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{F(s)}{s}\bigr\}$ by considering contour integration with different entire functions $F(s)$

laplace-transform contour-integration

Jan 2 '15 at 5:30 dustin 7,669

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36 Questions

About the great result of $\int\underbrace{x^{x^{\cdot^{\cdot^x}}}}_m~dx$

$\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$

How to find the general solution of $xy''-(2x+1)y'+x^2y=0$ when we know the general solution of $y''+2y'+xy=0$?

Why solving $\dfrac{\partial u}{\partial x}=\dfrac{\partial^2u}{\partial y^2}$ like this is wrong?

How to solve the nonlinear higher-order PDEs with overdetermined quantities of conditions whose their most-general solutions are known?

About fractional differentiation under the integral sign

About finding the general solution of first-order totally nonlinear PDE with two independent variables

Is it possible for cosine functions to have Fourier sine series expressions or sine functions to have Fourier cosine series expressions?

About differentiation under the product integral sign

About the second-order linear ODEs with polynomial coefficients

Longest cylinder of specified radius in a given cuboid

fancy about some properties of kernel functions at infinity

Does solve PDE by combination of variables always cannot find the general solutions?

Iterations of $f(x)=\dfrac{ax+b}{cx+d}$

Properties about the Generalized Legendre-type polynomial sequence $f_n(x)=\frac{d^n}{dx^n}(p(x)^n)$

About the inverse laplace transform of sinc function

How to solve the PDEs with more than two independent variables whose their most-general solutions are known?

about discrete versions of “inverse laplace transform”

fancy about inverse discrete Fourier sine and cosine transform (i.e. Fourier sine and cosine series)

About the linear PDE $u_{x_1x_2x_3…x_n}=u$

How the change of variables of a PDE affects the given condition(s)?

How are the general skills for complete factorization of arbitrary homogeneous order polynomials in $\mathbb{C}$?

Properties about the Generalized Hermite-type polynomial sequence $f_n(x)=e^{-p(x)}\frac{d^n}{dx^n}e^{p(x)}$

Are there the resources mentioned about finding the general solutions of some first order fully nonlinear PDE examples by method of characteristics?

How to prove the periodicity of an iterated function?

Advanced improper integral involving periodic function of polynomial

How to compute the convolution of two functions which diverge at infinity?

Does Heun's differential equation have other known types confluent approach?

Evaluate $\sum\limits_{n=0}^\infty n^ke^{-an^2}$ and $\sum\limits_{n=0}^\infty(-1)^nn^ke^{-an^2}$ .

About evaluating $\mathcal{L}^{-1}_{s\to x}\bigl\{\frac{F(s)}{s}\bigr\}$ by considering contour integration with different entire functions $F(s)$