Question

Inverse formula for a function inside an integral.

score 169 · Answer 1 · 2021-09-20 17:05:10

169

Views

Inverse formula for a function inside an integral.

Published on 20 Sep 2021 - 17:05

score 168 · Answer 2 · 2021-10-22 19:05:54

168

Views

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

Published on 22 Oct 2021 - 19:05

score 127 · Answer 3 · 2021-10-29 07:39:54

127

Views

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

Published on 29 Oct 2021 - 7:39

score 197 · Answer 4 · 2021-11-23 21:53:47

197

Views

Lagrange inversion theorem and Legendre polynomials generating function

Published on 23 Nov 2021 - 21:53

score 396 · Answer 5 · 2021-12-01 23:29:53

396

Views

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

Published on 01 Dec 2021 - 23:29

score 603 · Answer 6 · 2022-02-09 00:58:15

603

Views

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

Published on 09 Feb 2022 - 0:58

score 149 · Answer 7 · 2022-04-08 18:12:37

149

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 08 Apr 2022 - 18:12

score 52 · Answer 8 · 2022-07-14 20:39:45

52

Views

Flajolet et al analytic combinatorics integral

Published on 14 Jul 2022 - 20:39

score 100 · Answer 9 · 2022-08-17 03:05:06

100

Views

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

Published on 17 Aug 2022 - 3:05

score 67 · Answer 10 · 2022-09-18 00:35:48

67

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 18 Sep 2022 - 0:35

score 52 · Answer 11 · 2022-10-12 20:48:59

52

Views

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

Published on 12 Oct 2022 - 20:48

score 113 · Answer 12 · 2022-11-01 00:36:26

113

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 01 Nov 2022 - 0:36

score 148 · Answer 13 · 2022-11-01 13:48:56

148

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 01 Nov 2022 - 13:48

score 130 · Answer 14 · 2022-11-05 12:46:14

130

Views

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

Published on 05 Nov 2022 - 12:46

score 113 · Answer 15 · 2022-11-15 02:28:20

113

Views

Extracting sequence from generating function

Published on 15 Nov 2022 - 2:28

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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