Question

Inverse formula for a function inside an integral.

score 170 · Answer 1 · 2026-02-24 08:36:23

170

Views

Inverse formula for a function inside an integral.

Published on 24 Feb 2026 - 8:36

score 169 · Answer 2 · 2026-02-24 08:36:38

169

Views

How is the combinatorist's Lagrange Inversion equivalent to the complex analytic expression of the same theorem?

Published on 24 Feb 2026 - 8:36

score 128 · Answer 3 · 2026-02-24 08:34:33

128

Views

How to calculate the inverse of $f(t) = \frac{(k/2)(\sin(t) + t) - t}{2π (k/2 - 1)}$?

Published on 24 Feb 2026 - 8:34

score 198 · Answer 4 · 2026-02-24 08:36:24

198

Views

Lagrange inversion theorem and Legendre polynomials generating function

Published on 24 Feb 2026 - 8:36

score 397 · Answer 5 · 2026-02-24 08:34:30

397

Views

Explicit series expansion for inverse of $e^{-x}\left(\frac{x^2}2+x+1\right)$

Published on 24 Feb 2026 - 8:34

score 604 · Answer 6 · 2026-02-24 08:33:13

604

Views

Functional inverse of $z=1+w+\cdots+w^{n-1}$

Published on 24 Feb 2026 - 8:33

score 150 · Answer 7 · 2026-02-24 08:34:32

150

Views

Why is the bizarre $f^{-1}(y)=y+\sum_{n=1}^\infty\frac{1}{n!}\frac{d^{n-1}}{dy^{n-1}}[y-f(y)]^n$ equivalent to the Lagrange inversion formula?

Published on 24 Feb 2026 - 8:34

score 53 · Answer 8 · 2026-02-24 08:36:40

53

Views

Flajolet et al analytic combinatorics integral

Published on 24 Feb 2026 - 8:36

score 101 · Answer 9 · 2026-02-24 08:31:27

101

Views

Finding the pattern of Lagrange Inversion Formula for $x+\sin x$

Published on 24 Feb 2026 - 8:31

score 68 · Answer 10 · 2026-02-24 08:34:28

68

Views

Solving $\frac{d^{n-1}}{da^{n-1}}(f^n(a)g’(a))=h(a,n)(n+u)^{vn},v<0$ from Lagrange reversion

Published on 24 Feb 2026 - 8:34

score 53 · Answer 11 · 2026-02-24 08:33:13

53

Views

Find coefficient in series expansion of $x^2C^3(x)$

Published on 24 Feb 2026 - 8:33

score 114 · Answer 12 · 2026-02-24 08:34:33

114

Views

Completing the explicit $\lim\limits_{c\to0}\text I^{-1}_{cx}(r,c)$/ inverse $\int_0^x\frac{t^{r-1}}{1-t}dt,r\in\Bbb Q$ series expansion

Published on 24 Feb 2026 - 8:34

score 149 · Answer 13 · 2026-02-24 08:35:22

149

Views

Prove $\sum_{n \ge 0} (n+1)^{n-1}\frac{x^n}{n!} =(1- \sum_{n \ge 1} (n-1)^{n-1} \frac{x^n}{n!}) ^{-1}$

Published on 24 Feb 2026 - 8:35

score 131 · Answer 14 · 2026-02-24 08:31:27

131

Views

Lagrange inversion theorem applied on $f(x)=x-x^p$

Published on 24 Feb 2026 - 8:31

score 114 · Answer 15 · 2026-02-24 08:36:26

114

Views

Extracting sequence from generating function

Published on 24 Feb 2026 - 8:36

List Question

Inverse formula for a function inside an integral.

How is the combinatorist's Lagrange Inversion equivalent to the complex analytic expression of the same theorem?

How to calculate the inverse of $f(t) = \frac{(k/2)(\sin(t) + t) - t}{2π (k/2 - 1)}$?

Lagrange inversion theorem and Legendre polynomials generating function

Explicit series expansion for inverse of $e^{-x}\left(\frac{x^2}2+x+1\right)$

Functional inverse of $z=1+w+\cdots+w^{n-1}$

Why is the bizarre $f^{-1}(y)=y+\sum_{n=1}^\infty\frac{1}{n!}\frac{d^{n-1}}{dy^{n-1}}[y-f(y)]^n$ equivalent to the Lagrange inversion formula?

Flajolet et al analytic combinatorics integral

Finding the pattern of Lagrange Inversion Formula for $x+\sin x$

Solving $\frac{d^{n-1}}{da^{n-1}}(f^n(a)g’(a))=h(a,n)(n+u)^{vn},v<0$ from Lagrange reversion

Find coefficient in series expansion of $x^2C^3(x)$

Completing the explicit $\lim\limits_{c\to0}\text I^{-1}_{cx}(r,c)$/ inverse $\int_0^x\frac{t^{r-1}}{1-t}dt,r\in\Bbb Q$ series expansion

Prove $\sum_{n \ge 0} (n+1)^{n-1}\frac{x^n}{n!} =(1- \sum_{n \ge 1} (n-1)^{n-1} \frac{x^n}{n!}) ^{-1}$

Lagrange inversion theorem applied on $f(x)=x-x^p$

Extracting sequence from generating function

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