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

Sine

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