Reputation
5,037
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
2 14 43
Impact
~172k people reached

Nov
4
revised To find the general formula of $\overbrace{g(g(g(…g(x))}^\text{n}=g_n(x)=\frac{A_{n}.x+B_{n}}{C_{n}.x+D_{n}}$
edited body
Nov
4
comment To find the general formula of $\overbrace{g(g(g(…g(x))}^\text{n}=g_n(x)=\frac{A_{n}.x+B_{n}}{C_{n}.x+D_{n}}$
It is very nice. I wonder something if it is possible to express $A_n,B_n,C_n,D_n $ as exponential functions as we can do for $F_n$ or not?
Nov
4
revised To find the general formula of $\overbrace{g(g(g(…g(x))}^\text{n}=g_n(x)=\frac{A_{n}.x+B_{n}}{C_{n}.x+D_{n}}$
added 153 characters in body
Nov
4
asked To find the general formula of $\overbrace{g(g(g(…g(x))}^\text{n}=g_n(x)=\frac{A_{n}.x+B_{n}}{C_{n}.x+D_{n}}$
Oct
20
awarded  Popular Question
Oct
13
accepted How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
Oct
13
comment How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
Really nice approach: I liked the way you used $Z(x)=e^x$ in $U$ Function . It made very easy proof and also thanks for generalized formula.
Oct
13
answered How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
Oct
10
revised How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
added 549 characters in body
Oct
10
comment How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
@marco trevi: It is the function that depends on x
Oct
10
revised How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
added 78 characters in body; edited title
Oct
10
asked How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Sep
22
awarded  Notable Question
Aug
14
answered Simple geometry problem
Aug
14
revised How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
deleted 1 character in body
Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@Winther Thanks a lot for comments. The final expression is very beautiful. I will focus on some examples to confirm .It can be used as a nice tool.
Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@ChristianBlatter $$ f(x)+\frac{y.f''(x)}{2!}+\frac{y^2 f^{(4)}(x)}{4!}+\cdots=\frac{1}{2} (e^{\sqrt{y}S}(f(x))+e^{-\sqrt{y}S}(f(x)))=\frac{1}{2}(f(x+\sqrt{y})+f(x-\sqrt{y‌​}))$$ but I am looking for a closed form of $ f(x)+\frac{y.f''(x)}{1!}+\frac{y^2 f^{(4)}(x)}{2!}+\cdots$ if we can express it as $\sum a_n(y)f(x+b_n(y))$ or not
Aug
14
comment How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
@Winther I updated as you commented. Is it correct what I got? It seems The form is an integral transform of that operator but no any relation for a linear f formula. Maybe I need to do some more transforms in last integral to get my aim. Thanks for advice