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Fungrim entry: 6b13be

sin ⁣(z+x)=k=0sin ⁣(z+πk2)xkk!\sin\!\left(z + x\right) = \sum_{k=0}^{\infty} \sin\!\left(z + \frac{\pi k}{2}\right) \frac{{x}^{k}}{k !}
Assumptions:zCandxCz \in \mathbb{C} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
\sin\!\left(z + x\right) = \sum_{k=0}^{\infty} \sin\!\left(z + \frac{\pi k}{2}\right) \frac{{x}^{k}}{k !}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Sumnf(n)\sum_{n} f(n) Sum
ConstPiπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("6b13be"),
    Formula(Equal(Sin(Add(z, x)), Sum(Mul(Sin(Add(z, Div(Mul(ConstPi, k), 2))), Div(Pow(x, k), Factorial(k))), For(k, 0, Infinity)))),
    Variables(z, x),
    Assumptions(And(Element(z, CC), Element(x, CC))))

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2019-10-05 13:11:19.856591 UTC