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Discover LudwigExact(16)
Let S be the subclass of A consisting of univalent functions [1].
We denote by K the subclass of A consisting of functions which are convex of order α in U (see, [1, 2]).
Also, let S and K denote the subclasses of A consisting of functions which are, respectively, univalent and convex in U.
Let S ∗ and C denote the subclasses of A consisting of starlike and convex functions of order α ( 0 ≤ α < 1 ) in U, respectively.
Let S be the subclass of A consisting of univalent functions in U with the normalized condition f ( 0 ) = 0 = f ′ ( 0 ) − 1.
Now, let A θ denotes the subclass of A consisting of functions f (z) with a n = a n e i ( ( n - 1 ) θ + π ) ( n = 2, 3,... ).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com