# Fungrim entry: bf8f37

Symbol: CurvePath $\left(f(t),\, t : a \rightsquigarrow b\right)$ Path along a curve
CurvePath(f(t), For(t, a, b)) $\left(f(t),\, t : a \rightsquigarrow b\right)$ Represents the path traced by $f(t)$ as $t$ follows the path $a \rightsquigarrow b$.
CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Mul(2, Pi))) $\left(R {e}^{i t},\, t : 0 \rightsquigarrow 2 \pi\right)$ Represents the circular path counterclockwise around the origin, starting at $R$.
CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Neg(Mul(2, Pi)))) $\left(R {e}^{i t},\, t : 0 \rightsquigarrow -2 \pi\right)$ Represents the circular path clockwise around the origin, starting at $R$.
Path(Pos(Infinity), CurvePath(Exp(Mul(ConstI, t)), For(t, Div(Pi, 2), Div(Mul(3, Pi), 2))), Pos(Infinity)) $+\infty \rightsquigarrow \left({e}^{i t},\, t : \pi / 2 \rightsquigarrow 3 \pi / 2\right) \rightsquigarrow +\infty$ Represents the Hankel contour starting at $+\infty$, moving along a straight line above the real axis to $i$, moving in a half-circle around the origin to $-i$, and returning to $+\infty$ along a straight line below the real axis.
Definitions:
Fungrim symbol Notation Short description
CurvePath$\left(f(t),\, t : a \rightsquigarrow b\right)$ Path along a curve
Path$a \rightsquigarrow b \rightsquigarrow c$ Line path
Exp${e}^{z}$ Exponential function
ConstI$i$ Imaginary unit
Pi$\pi$ The constant pi (3.14...)
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("bf8f37"),
SymbolDefinition(CurvePath, CurvePath(f(t), For(t, a, b)), "Path along a curve"),
CodeExample(CurvePath(f(t), For(t, a, b)), "Represents the path traced by", f(t), "as", t, "follows the path", Path(a, b), "."),
CodeExample(CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Mul(2, Pi))), "Represents the circular path counterclockwise around the origin, starting at", R, "."),
CodeExample(CurvePath(Mul(R, Exp(Mul(ConstI, t))), For(t, 0, Neg(Mul(2, Pi)))), "Represents the circular path clockwise around the origin, starting at", R, "."),
CodeExample(Path(Pos(Infinity), CurvePath(Exp(Mul(ConstI, t)), For(t, Div(Pi, 2), Div(Mul(3, Pi), 2))), Pos(Infinity)), "Represents the Hankel contour starting at", Pos(Infinity), ", moving along a straight line above the real axis to", i, ", moving in a half-circle around the origin to", Neg(i), ", and returning to", Pos(Infinity), "along a straight line below the real axis."))

## 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