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Fungrim entry: eb1d4f

RC ⁣(1,1+y)={atan⁡ ⁣(y)y,y≠01,y=0R_C\!\left(1, 1 + y\right) = \begin{cases} \frac{\operatorname{atan}\!\left(\sqrt{y}\right)}{\sqrt{y}}, & y \ne 0\\1, & y = 0\\ \end{cases}
Assumptions:y∈Cy \in \mathbb{C}
TeX:
R_C\!\left(1, 1 + y\right) = \begin{cases} \frac{\operatorname{atan}\!\left(\sqrt{y}\right)}{\sqrt{y}}, & y \ne 0\\1, & y = 0\\ \end{cases}

y \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
CarlsonRCRC ⁣(x,y)R_C\!\left(x, y\right) Degenerate Carlson symmetric elliptic integral of the first kind
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("eb1d4f"),
    Formula(Equal(CarlsonRC(1, Add(1, y)), Cases(Tuple(Div(Atan(Sqrt(y)), Sqrt(y)), NotEqual(y, 0)), Tuple(1, Equal(y, 0))))),
    Variables(y),
    Assumptions(Element(y, CC)))

Topics using this entry

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