Question

Proving a series satisfies a particular functional equation.

score 86 · Answer 1 · 2020-06-12 01:21:17

86

Views

Proving a series satisfies a particular functional equation.

Published on 12 Jun 2020 - 1:21

score 219 · Answer 2 · 2020-06-26 15:17:29

219

Views

When does the limiting ratio of the coefficients in the series expansion of the reciprocal of a polynomial give the first real root of the polynomial?

Published on 26 Jun 2020 - 15:17

score 1k · Answer 3 · 2016-11-18 21:58:17

1k

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Solving $x^p-x-1=0$ with Lagrange Inversion Formula

Published on 18 Nov 2016 - 21:58

score 99 · Answer 4 · 2016-12-28 03:58:36

99

Views

Extending an Analytic Proof for Lagrange Inversion of Formal Power Series

Published on 28 Dec 2016 - 3:58

score 421 · Answer 5 · 2017-01-21 22:31:58

421

Views

Lagrange Inversion - Analytic to Formal Power Series

Published on 21 Jan 2017 - 22:31

score 317 · Answer 6 · 2017-02-14 09:16:02

317

Views

Inversion of so-called probability-generating functional

Published on 14 Feb 2017 - 9:16

score 174 · Answer 7 · 2017-02-19 01:36:02

174

Views

Invert an odd-symmetry function of one variable (with a parameter) using two terms and Lagrange Inversion Theorem.

Published on 19 Feb 2017 - 1:36

score 76 · Answer 8 · 2017-03-15 19:23:31

76

Views

Isabelle -- Strange proof under Formal_Power_Series

Published on 15 Mar 2017 - 19:23

score 200 · Answer 9 · 2017-03-26 22:19:54

200

Views

Functions satsify $f'=f^{-1}$ with $f^{-1}$ is compostional inverse of$ f$

Published on 26 Mar 2017 - 22:19

score 174 · Answer 10 · 2023-04-14 13:00:25

174

Views

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

Published on 14 Apr 2023 - 13:00

score 33 · Answer 11 · 2023-04-22 19:12:15

33

Views

Evaluate $\frac{d^{n-1}}{dw^{n-1}}\csc^{-1}(w)^n$ or $\frac{d^{n-1}}{dw^{n-1}}\left(\frac{\sqrt{w^2-1}+i}w-1\right)^m$

Published on 22 Apr 2023 - 19:12

score 71 · Answer 12 · 2023-05-10 01:58:21

71

Views

Series reversion of polynomial using Bürmann-Lagrange series

Published on 10 May 2023 - 1:58

score 96 · Answer 13 · 2023-05-21 02:24:13

96

Views

Evaluating $\frac{d^n}{dt^n}e^{a(t-e^t)}$ as a single series to extend region of convergence for super root function

Published on 21 May 2023 - 2:24

score 35 · Answer 14 · 2023-07-10 09:57:16

35

Views

Reference for Lagrange inversion formula

Published on 10 Jul 2023 - 9:57

score 72 · Answer 15 · 2023-07-28 13:26:20

72

Views

Multivariate function inversion - Lagrange Inversion

Published on 28 Jul 2023 - 13:26

List Question

Proving a series satisfies a particular functional equation.

When does the limiting ratio of the coefficients in the series expansion of the reciprocal of a polynomial give the first real root of the polynomial?

Solving $x^p-x-1=0$ with Lagrange Inversion Formula

Extending an Analytic Proof for Lagrange Inversion of Formal Power Series

Lagrange Inversion - Analytic to Formal Power Series

Inversion of so-called probability-generating functional

Invert an odd-symmetry function of one variable (with a parameter) using two terms and Lagrange Inversion Theorem.

Isabelle -- Strange proof under Formal_Power_Series

Functions satsify $f'=f^{-1}$ with $f^{-1}$ is compostional inverse of$ f$

Convert $\frac1b\sum_{n=1}^\infty\frac{(b e^a)^n}{n!}B_{n-1}(an)$ to integral using $B_n(x)=\frac{n!}{2\pi i}\oint\frac{e^{x(e^t-1)}}{t^{n+1}}dt$

Evaluate $\frac{d^{n-1}}{dw^{n-1}}\csc^{-1}(w)^n$ or $\frac{d^{n-1}}{dw^{n-1}}\left(\frac{\sqrt{w^2-1}+i}w-1\right)^m$

Series reversion of polynomial using Bürmann-Lagrange series

Evaluating $\frac{d^n}{dt^n}e^{a(t-e^t)}$ as a single series to extend region of convergence for super root function

Reference for Lagrange inversion formula

Multivariate function inversion - Lagrange Inversion

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