I am an engineer who is in love with math and lifelong math student. I love to learn new things in mathematics for self-satisfaction. My idols are Gauss , Euler , Ramanujan because they were in love with math as I feel.

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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
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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 $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
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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 $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
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Oct
10
asked How to find sum of coefficients of $\frac{d^n}{dx^n} \left( Z(x)^m \right)$
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answered Simple geometry problem
Aug
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revised How to express $e^{yS^2}(f(x))$ in closed form where $\frac{d}{dx}=S$
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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
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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
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