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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:zC  and  xCz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
\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}
Fungrim symbol Notation Short description
Sinsin(z)\sin(z) Sine
Sumnf(n)\sum_{n} f(n) Sum
Piπ\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:
    Formula(Equal(Sin(Add(z, x)), Sum(Mul(Sin(Add(z, Div(Mul(Pi, 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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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC