Question

How helpful is $f^{-1}(z)=\frac1{2\pi i}\oint\ln(1-\frac z{f(w)})dw$, or the method to find it, in deriving integral representations of $f^{-1}(z)$?

score 118 · Answer 1 · 2026-02-24 07:07:38

118

Views

How helpful is $f^{-1}(z)=\frac1{2\pi i}\oint\ln(1-\frac z{f(w)})dw$, or the method to find it, in deriving integral representations of $f^{-1}(z)$?

Published on 24 Feb 2026 - 7:07

score 35 · Answer 2 · 2026-03-25 12:53:30

35

Views

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score 107 · Answer 3 · 2026-03-27 16:39:16

107

Views

parametric reflection of one curve across another

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score 28 · Answer 4 · 2026-03-26 21:35:11

28

Views

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score 52 · Answer 5 · 2026-03-26 21:27:05

52

Views

Can we solve $u=(x^4+y^4)/x,v=\sin x+\cos y$ for $(x,y)$ near $(\pi/2,\pi/2)$?

Published on 26 Mar 2026 - 21:27

score 46 · Answer 6 · 2024-03-06 14:46:02

46

Views

Inverse of a piecewise floor function

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score 738 · Answer 7 · 2026-03-25 19:06:36

738

Views

Find the center of all circles that touch the $x$-axis and a circle centered at the origin

Published on 25 Mar 2026 - 19:06

score 38 · Answer 8 · 2024-03-13 07:27:11

38

Views

About continuity of $f^{-1}$.

Published on 13 Mar 2024 - 7:27

score 54 · Answer 9 · 2026-03-25 06:01:56

54

Views

Unclear step in the proof of Inverse Function Theorem

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score 55 · Answer 10 · 2024-03-16 15:14:55

55

Views

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score 58 · Answer 11 · 2024-03-19 08:43:52

58

Views

How to prove continuity of the inverse function $\alpha^{-1}$ in general?

Published on 19 Mar 2024 - 8:43

score 29 · Answer 12 · 2024-03-21 18:41:28

29

Views

Let $f:V'\rightarrow V$ be a linear function and $A$ be an affine subspace in V, then $f^{-1}(A)$ is an affine subspace in $V'$

Published on 21 Mar 2024 - 18:41

score 71 · Answer 13 · 2024-03-26 21:00:27

71

Views

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Published on 26 Mar 2024 - 21:00

score 44 · Answer 14 · 2024-03-28 22:21:51

44

Views

Coefficients of the Inverse Modified Bessel Function

Published on 28 Mar 2024 - 22:21

score 21k · Answer 15 · 2015-02-12 18:19:32

21k

Views

Does a function need to be either surjective, injective, or bijective to be invertible?

Published on 12 Feb 2015 - 18:19

List Question

How helpful is $f^{-1}(z)=\frac1{2\pi i}\oint\ln(1-\frac z{f(w)})dw$, or the method to find it, in deriving integral representations of $f^{-1}(z)$?

How to invert system of multivariable polynomial equations for dependent variables

parametric reflection of one curve across another

How to get inverse function of x-sin(ax)

Can we solve $u=(x^4+y^4)/x,v=\sin x+\cos y$ for $(x,y)$ near $(\pi/2,\pi/2)$?

Inverse of a piecewise floor function

Find the center of all circles that touch the $x$-axis and a circle centered at the origin

About continuity of $f^{-1}$.

Unclear step in the proof of Inverse Function Theorem

Problem about inverse function and derivative

How to prove continuity of the inverse function $\alpha^{-1}$ in general?

Let $f:V'\rightarrow V$ be a linear function and $A$ be an affine subspace in V, then $f^{-1}(A)$ is an affine subspace in $V'$

Upper bound for series with $\arcsin$, $\arccos$ and $\arctan$

Coefficients of the Inverse Modified Bessel Function

Does a function need to be either surjective, injective, or bijective to be invertible?

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