I asked wolfram alpha to compute the antiderivative of the function $x^x$. It gave me some really large confusing polynomial-esque thing called a puiseux series. However, from what I can gather on the internet, the puiseux series is used to approximate points on a function. So what is the puiseux series and what does it have to do with integration? Also could you please explain it so that it would be understandable by someone who's highest mathematics taken was calculus BC.
2026-03-26 13:00:59.1774530059
What is a puiseux series and what is wolfram-alpha doing with this antiderivative?
789 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- Proving the differentiability of the following function of two variables
- If $f ◦f$ is differentiable, then $f ◦f ◦f$ is differentiable
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Number of roots of the e
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- How to prove $\frac 10 \notin \mathbb R $
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
Related Questions in INTEGRATION
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- How to integrate $\int_{0}^{t}{\frac{\cos u}{\cosh^2 u}du}$?
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- How to find the unit tangent vector of a curve in R^3
- multiplying the integrands in an inequality of integrals with same limits
- Closed form of integration
- Proving smoothness for a sequence of functions.
- Random variables in integrals, how to analyze?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Which type of Riemann Sum is the most accurate?
Related Questions in SEQUENCES-AND-SERIES
- How to show that $k < m_1+2$?
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Negative Countdown
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Show that the sequence is bounded below 3
- A particular exercise on convergence of recursive sequence
- Proving whether function-series $f_n(x) = \frac{(-1)^nx}n$
- Powers of a simple matrix and Catalan numbers
- Convergence of a rational sequence to a irrational limit
- studying the convergence of a series:
Related Questions in TETRATION
- How to solve $ax^x+bx+c=0$?
- Why is $\underbrace {i^{i^{i^{.^{.^{.^{i}}}}}}}_{n \ times}$ converging?
- Is there a Tetration Function?
- $w =\operatorname{arcsinh}(1+2\operatorname{arcsinh}(1+2^2\operatorname{arcsinh}(1+2^{2^2}\operatorname{arcsinh}(1+\dotsm$
- $f(x) = \sqrt x^{{\sqrt[3]{x}}^{\sqrt[4]{x},\cdots}}$ asymptotic?
- What is $\underbrace{2018^{2018^{2018^{\mathstrut^{.^{.^{.^{2018}}}}}}}}_{p\,\text{times}}\pmod p$ where $p$ is an odd prime?
- iterative solution of $x^x=a$
- What is the value of $i^{i^{i^{\cdots}}}$
- Finding a function satisfies $\ln F(x+1)=a F(x)$
- $f(exp(z)) = f(z) \cdot g(z) $ with closed form solutions?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
A Puiseux series is formal Laurent power series in $T^{\frac1n}$ for some $n$ (the $n$ may vary with the series). The set of Puiseux series is a field, denoted $k{\ll} T{\gg}$, and it is the algebraic closure of the field of formal power series $k[[T]]$.