# Search results

1. ### Derivative question

Thanks for you're answer. I suppose like ##df(x,y)=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy## special case ##\frac{df}{dx}dx=df(x)##
2. ### Derivative question

Is then in eq ##y'(x)=y(x)##, ##y(x)## value of function or function? :D Question for WannabeNewton. micromass ok called whatever you want. Why isn't equal ##df=\frac{df}{dx}##?
3. ### Derivative question

I didn't asked that. I asked why we can multiply and devide with ##dx##.
4. ### Derivative question

If ##f=f(x)## why then is ##df=\frac{df}{dx}dx##?
5. ### Divergence question

Yes. But I'm not sure why is that correct? Could you explain me that?
6. ### Divergence question

I see identity in one mathematical book div \vec{A}(r)=\frac{\partial \vec{A}}{\partial r} \cdot grad r How? From which equation?
7. ### Hypergeometric function

#_2F_1(a,b;c;x)# converge for #|x|<1#. Ok so I know that from this hypergeometric function I could define Legendre polynomials because they are defined for #|x|<1#. From Safari file P_n(x)=_2F_1(-n,n+1;1;\frac{1-x}{2}) From this table I see that T_n(x)=_2F_1(-n,n;\frac{1}{2};\frac{1-x}{2})...
8. ### Hypergeometric function

??? I don't understand why. J. Jacquelin I didn't get the answer from reading your text. How you get connection between Legendre polynomial and #_2F_1#?
9. ### Taylor series

Why in Taylor series we have some factoriel ##!## factor. f(x)=f(0)+xf'(0)+\frac{x^2}{2!}f''(0)+... Why we have that ##\frac{1}{n!}## factor?
10. ### Hypergeometric function

Tnx a lot for usefull answer. All hypergeometric function converge for ##|x|<1##. Right? So for example \ln (1+x)=x_2F_1(1,1;2;-x) This is correct for which ##x##? Only for ##|x|<1##. Right? I don't understand jet why those functions are so important. Ok for example I want to know Legendre...
11. ### Hypergeometric function

Thanks a lot for your answer. One more short question. "The confluent hypergeometric functions are degenerate hypergeometric functions." Why? I don't see that. Confluent hypergeometric function is ##F(a;b;x)## and hypergeometric function is ##F(a,b;c,x)##. Why ##F(a;b;x)## is called...
12. ### Hypergeometric function

Hypergeometric function is defined by: _2F_1(a,b,c,x)=\sum^{\infty}_{n=0}\frac{(a)_n(b)_n}{n!(c)_n}x^n where ##(a)_n=a(a+1)...(a+n-1)##... I'm confused about this notation in case, for example, ##_2F_1(-n,b,b,1-x)##. Is that _2F_1(-n,b,b,1-x)=\sum^{\infty}_{n=0}\frac{(-n)_n}{n!}(1-x)^n or...
13. ### Infinite sum question

Happy new year. All the best. I have one question. Is it true? \sum^{\infty}_{k=0}a_kx^k=\sum^n_{k=0}a_{n-k}x^{n-k} I saw in one book relation \sum^{\infty}_{k=0}\frac{(2k)!}{2^{2k}(k!)^2}(2xt-t^2)^k=\sum^{n}_{k=0}\frac{(2(n-k))!}{2^{2(n-k)}((n-k)!)^2}(2xt-t^2)^{n-k} Can you give me some...
14. ### Poisson kernel

Well ok. But for example what you get if you multiplying ##P_r(\theta)\sin\theta##? Or ##P^2_r(\theta)\sin\theta##? Thx for your answer. I know about that.
15. ### Poisson kernel

Why Poisson kernel is significant in mathematics? Poisson kernel is ##P_r(\theta)=\frac{1-r^2}{1-2rcos\theta+r^2}##. http://www.math.umn.edu/~olver/pd_/gf.pdf [Broken] page 218, picture 6.15. If we have some function for example ##e^x,sinx,cosx## what we get if we multiply that function with...
16. ### Fredholm integral equation

Is there any way to solve Fredholm integral equation without using Fourier transform. \varphi(t)=f(t)+\lambda\int^b_aK(t,s)\varphi(s)ds?
17. ### Laplace transform limits?

For ##1## both sides are equal ##1##. ##lim_{t\to \infty}1=1=lim_{p\to 0}p\frac{1}{p}=1##. I think that is correct only if both limits converge.
18. ### Laplace transform limits?

I saw also assymptotics relation ##\lim_{t \to \infty}f(t)=\lim_{p\to 0}pF(p)## when that relation is valid?
19. ### Inverse Laplace transform

Can you give me a explanation why all singularities are left from ##Re(s)=c##? And why we integrate over the line ##(c-i\infty,c+i\infty)##?
20. ### Laplace transform limits?

How we get relation \lim_{t\to 0}f(t)=\lim_{p\to \infty}pF(p)? Where ##\mathcal{L}\{f\}=F##.
21. ### Laplace transform converge

##\mathcal{L}\{f(t)\}=F(s)## \mathcal{L}\{e^{at}\}=\frac{1}{s-a},Re(s)>a \mathcal{L}\{\sin (at)\}=\frac{a}{s^2+a^2}, \quad Re(s)>0 \mathcal{L}\{\cos (at)\}=\frac{s}{s^2+a^2},Re(s)>0 If we look at Euler identity ##e^{ix}=\cos x+i\sin x##, how to get difference converge intervals...
22. ### Laplace transform question

Ok. Tnx. Do you know how to prove? ##F(s)*G(s)=f(t)g(t)##?
23. ### Laplace transform question

Sorry but I see here only convolution of originals.

25. ### Laplace transform question

\mathcal{L}\{f(t)*g(t)\}=F(s)G(s) Is there some relation between F(s)*G(s) and f(t)g(t)? ##*## is convolution.
26. ### Gauss theorem

Here is the picture
27. ### Gauss theorem

\oint_S \vec{A}\cdot d\vec{S}=\int_V div\vec{A}dv Suppose region where \vec{A}(\vec{r}) is diferentiable everywhere except in region which is given in the picture. Around this region is surface S'. In this case Gauss theorem leads us to \int_S \vec{A}\cdot d\vec{S}+\int_S \vec{A}\cdot...
28. ### Total variation

What's difference between total derivative, and total variation?
29. ### Total variation

Total variation is defined by \Delta f=\delta f+\Delta x For example f(x,y)=yx, y=y(x) \Delta f=x\delta y+\Delta x How is defined \Delta x. Is that rate of change of x, while y is constant?
30. ### Variation question

I mean by variation infinitesimal change of function while argument stay fiksed. \varphi(x) \bar{\varphi}(x) variation \delta \varphi(x)=\bar{\varphi}(x)-\varphi(x)