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Fungrim entry: 65c610

ex+y=k=0n=0(n+kk)xkyn(n+k)!{e}^{x + y} = \sum_{k=0}^{\infty} \sum_{n=0}^{\infty} {n + k \choose k} \frac{{x}^{k} {y}^{n}}{\left(n + k\right)!}
Assumptions:xC  and  yCx \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}
{e}^{x + y} = \sum_{k=0}^{\infty} \sum_{n=0}^{\infty} {n + k \choose k} \frac{{x}^{k} {y}^{n}}{\left(n + k\right)!}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; y \in \mathbb{C}
Fungrim symbol Notation Short description
Expez{e}^{z} Exponential function
Sumnf(n)\sum_{n} f(n) Sum
Binomial(nk){n \choose k} Binomial coefficient
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Exp(Add(x, y)), Sum(Sum(Mul(Binomial(Add(n, k), k), Div(Mul(Pow(x, k), Pow(y, n)), Factorial(Add(n, k)))), For(n, 0, Infinity)), For(k, 0, Infinity)))),
    Variables(x, y),
    Assumptions(And(Element(x, CC), Element(y, CC))))

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2021-03-15 19:12:00.328586 UTC