# Fungrim entry: 6b13be

$\sin\!\left(z + x\right) = \sum_{k=0}^{\infty} \sin\!\left(z + \frac{\pi k}{2}\right) \frac{{x}^{k}}{k !}$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}$
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
Sin$\sin(z)$ Sine
Sum$\sum_{n} f(n)$ Sum
Pi$\pi$ The constant pi (3.14...)
Pow${a}^{b}$ Power
Factorial$n !$ Factorial
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("6b13be"),
Formula(Equal(Sin(Add(z, x)), Sum(Mul(Sin(Add(z, Div(Mul(Pi, k), 2))), Div(Pow(x, k), Factorial(k))), For(k, 0, Infinity)))),
Variables(z, x),
Assumptions(And(Element(z, CC), Element(x, CC))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC