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Fungrim entry: bad502

ec+z=eck=0zkk!{e}^{c + z} = {e}^{c} \sum_{k=0}^{\infty} \frac{{z}^{k}}{k !}
Assumptions:cCandzCc \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
TeX:
{e}^{c + z} = {e}^{c} \sum_{k=0}^{\infty} \frac{{z}^{k}}{k !}

c \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Expez{e}^{z} Exponential function
Sumnf(n)\sum_{n} f(n) Sum
Powab{a}^{b} Power
Factorialn!n ! Factorial
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("bad502"),
    Formula(Equal(Exp(Add(c, z)), Mul(Exp(c), Sum(Div(Pow(z, k), Factorial(k)), For(k, 0, Infinity))))),
    Variables(c, z),
    Assumptions(And(Element(c, CC), Element(z, CC))))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC