User doraemonpaul

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8

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1

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285

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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 2,978

4

8

votes

1

answer

481

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 13.2k

2

7

votes

3

answers

1k

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

507

views

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

pde fake-proofs

Jul 9 '12 at 4:08 Community♦ 1

1

5

votes

0

answers

280

views

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

pde

Mar 31 '13 at 21:00 Community♦ 1

2

5

votes

1

answer

401

views

About fractional differentiation under the integral sign

fractional-calculus

Aug 3 '12 at 7:33 draks ... 11.6k

3

4

votes

1

answer

709

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

pde

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 30.6k

4

votes

1

answer

214

views

About differentiation under the product integral sign

calculus definite-integrals

Aug 1 '12 at 22:41 Henry T. Horton 15.4k

3

votes

3

answers

363

views

Longest cylinder of specified radius in a given cuboid

geometry

Jul 5 '15 at 4:18 Harish Chandra Rajpoot 29.8k

3

votes

0

answers

94

views

fancy about some properties of kernel functions at infinity

analysis definite-integrals integral-transforms

Apr 15 '13 at 4:51 doraemonpaul 13.2k

1

3

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1

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2k

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

pde

Apr 3 '13 at 13:49 Community♦ 1

2

votes

0

answers

45

views

About the second-order linear ODEs with polynomial coefficients

ordinary-differential-equations

Nov 29 '15 at 19:14 doraemonpaul 13.2k

2

votes

1

answer

103

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 473

2

votes

0

answers

623

views

About the inverse laplace transform of sinc function

laplace-transform contour-integration

Apr 10 '13 at 3:58 doraemonpaul 13.2k

2

votes

0

answers

146

views

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

pde

Mar 31 '13 at 21:10 Community♦ 1

2

votes

1

answer

165

views

about discrete versions of “inverse laplace transform”

laplace-transform

Dec 3 '12 at 12:04 doraemonpaul 13.2k

2

votes

3

answers

142

views

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

functional-equations function-and-relation-composition

Nov 19 '12 at 16:54 alex.jordan 40k

1

2

votes

1

answer

607

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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 13.2k

1

vote

0

answers

33

views

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

pde

Nov 17 '17 at 15:49 doraemonpaul 13.2k

1

vote

0

answers

57

views

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

pde

Mar 30 '14 at 0:38 Ellya 9,667

1

vote

0

answers

97

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 13.2k

1

vote

0

answers

74

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 13.2k

1

vote

0

answers

60

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 pde

Jan 24 '13 at 2:43 Community♦ 1

1

vote

1

answer

80

views

How to prove the periodicity of an iterated function?

periodic-functions function-and-relation-composition

Nov 20 '12 at 4:05 uncookedfalcon 3,674

1

vote

1

answer

362

views

Advanced improper integral involving periodic function of polynomial

calculus real-analysis improper-integrals

Nov 9 '12 at 5:37 Lukas Geyer 14k

1

vote

1

answer

414

views

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

convolution

Nov 1 '12 at 19:51 Robert Israel 337k

0

votes

0

answers

43

views

advance techniques for converting second-order linear ODEs with rational function coefficients to some known ODE types

ordinary-differential-equations

Mar 31 at 7:10 doraemonpaul 13.2k

1

0

votes

2

answers

101

views

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

ordinary-differential-equations

Nov 21 at 17:45 Przemo 4,906

0

votes

0

answers

62

views

About an Abel equation of the second kind in the canonical form $y\dfrac{dy}{dx}=y+a\sqrt{x}+b+\dfrac{c}{\sqrt{x}}$

ordinary-differential-equations

Aug 10 at 13:04 doraemonpaul 13.2k

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38 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

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?

About the second-order linear ODEs with polynomial coefficients

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”

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

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?

advance techniques for converting second-order linear ODEs with rational function coefficients to some known ODE types

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

About an Abel equation of the second kind in the canonical form $y\dfrac{dy}{dx}=y+a\sqrt{x}+b+\dfrac{c}{\sqrt{x}}$