What methods exist to computationally determine the first $k$ coefficients of a function (possibly polynomial or rational polynomial function)?
How do Mathematica/MatLab/Maple/etc. solve this problem?
Thanks!
2026-03-26 19:05:40.1774551940
Computational complexity of expanding a MacLaurin/Taylor Series
130 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in TAYLOR-EXPANSION
- Mc Laurin and his derivative.
- Maclaurin polynomial estimating $\sin 15°$
- why can we expand an expandable function for infinite?
- Solving a limit of $\frac{\ln(x)}{x-1}$ with taylor expansion
- How to I find the Taylor series of $\ln {\frac{|1-x|}{1+x^2}}$?
- Proving the binomial series for all real (complex) n using Taylor series
- Taylor series of multivariable functions problem
- Taylor series of $\frac{\cosh(t)-1}{\sinh(t)}$
- The dimension of formal series modulo $\sin(x)$
- Finding Sum of First Terms
Related Questions in COMPUTATIONAL-COMPLEXITY
- Product of sums of all subsets mod $k$?
- Proving big theta notation?
- Little oh notation
- proving sigma = BigTheta (BigΘ)
- sources about SVD complexity
- Is all Linear Programming (LP) problems solvable in Polynomial time?
- growth rate of $f(x)= x^{1/7}$
- Unclear Passage in Cook's Proof of SAT NP-Completeness: Why The Machine M Should Be Modified?
- Minimum Matching on the Minimum Triangulation
- How to find the average case complexity of Stable marriage problem(Gale Shapley)?
Related Questions in GENERATING-FUNCTIONS
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- How to multiply generating functions with $x^n$ and $x^{5n}$ and $x^{2n}$
- Relationship between the generating functions of sequences $(a_n),(b_n)$ given $b_n=\sum^n_{i=1}a_i$.
- Double-exponential sum (maybe it telescopes?)
- Solve recurrence equation: $a_{n}=(n-1)(a_{n-1}+a_{n-2})$
- Want to use Herbert Wilf's snake oil method to show $\sum_k \binom{2n+1}{2k}\binom{m+k}{2n} = \binom{2m+1}{2n}$
- Young Tableaux generating function
- Generating function of the sequence $\binom{2n}{n}^3H_n$
- Expansion of fibonacci generating function
- Partial fraction of $A(x)=\frac{x^2+x+1}{(1-x)^3}$
Related Questions in COMPUTATIONAL-MATHEMATICS
- The equivalent of 'quantum numbers' for a mathematical problem
- Skewes' number, and the smallest $x$ such that $\pi(x) > \operatorname{li}(x) - \tfrac1n \operatorname{li}(x^{1/2})$?
- Approximating a derivative through Newton interpolation
- What is the value of $2x+3y$?
- Good free calculator for manipulating symbolic matrices of 6x6 and larger?
- How to convert an approximation of CCDF for a standard normal to an approximation with a different mean and variance?
- Simple recursive algorithms to manually compute elementary functions with pocket calculators
- Asymptotic notation proof
- Graph layout that reflects graph symmetries
- What is the most efficient computation of the permanent?
Related Questions in COMPUTER-ALGEBRA-SYSTEMS
- List Conjugacy Classes in GAP?
- open-source illustrations of Riemann surfaces
- Entry systems for math that are simpler than LaTeX
- calculation of multiplicity of a subvariety
- Recursion relations: Coding a procedure to compute the number of planar rooted bipartite graphs
- Changing basis of indeterminates in polynomial ring
- Monster coefficients
- Use MuPAD to prove $(4^{(x-1)}+2^{(2x-4)})/(2^{(2x+1)}+5\cdot(2^{(2x-3)}))=5/42$
- Solve the following system of equations: $[x[i-1]-(2-h^2)x[i]+x[i+1]=0, \ x[1]=1, \ x[50]-x[49]=h$, where $h=0.1$
- Investigating the subgroup structure of $SL_{3}(\mathbb{Z}/4\mathbb{Z})$
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?
You might want to take a peek at maxima, an open-source computer algebra system. It is written in Common LISP, so be warned.
In general, I suspect that they do it more or less how you'd do it: If it is something known (and a CAS can have a huge list of known functions), use that, else build up the expansion by splicing together known expansions. Or just use Taylor's theorem, differentiating lots of times. But I'm sure some expert in symbolic computation will soon tell you I'm completely off-base...