# Questions tagged [approximation]

Questions on approximating functions (e.g. PadeApproximant), approximating integrals, working with approximate values (e.g. RootApproximant) etc.

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### How to invert this function when the argument e is small?

I need to find an analytical solution the following equation for e in terms of n and p ...
1 vote
55 views

### Graph lines do not show dashes [closed]

I have the following code of an iteration: ...
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### How to treat small numbers in order to gain efficiency and precision in neural network algorithm?

Unfortunately I won't be able to provide a MWE, as it would be too big and complex, and this question will be based on pure semantics, basically (and I understand if this is impossible to answer in ...
61 views

### How to ask Mathematica to give me possible closed forms from a given numerical approximation

Imagine I am solving a some Infinite Series and I cannot directly compute the value using Mathematica. The value of this series approximates $0.785398....$ (Actually is $\frac{\pi}{4}$). I want to be ...
75 views

### Calculation of Approximate Equation with Mathematica

I am trying to find an approximate equation for a complicated expression (L1, L2) using Mathematica. The equation involves several parameters and expressions, and I want to simplify it by considering ...
75 views

### How to obtain approximate form for a calculation using Mathematica with specific approximations?

I am currently working on a calculation in Mathematica that involves various parameters, including Nb, k, and Ns. I want to obtain an approximate form of the calculation by considering the following ...
60 views

### Approximate an expression with condition

I do the following computation: ...
110 views

### How to find an approximate equation from a given equation using Mathematica? [closed]

I am interested in finding an approximate equation based on a given equation using Mathematica. Specifically, I am working with the quantum illumination transmitter's quantum Chernoff bound (...
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### Approximation of the Fabius function with a quotient of exponentials

Approximation of the Fabius function $f(x) = \text{FabiusF}[x+1]\cdot \text{HeavisideTheta}[1-x^2]$ - FabiusF[x] doesn't work in Wolfram-Alpha I am looking to figure out how well the displaced version ...
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1 vote
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### Representing a number in r0 + r1 E + r2 E^2 form

Let E be the base of natural logarithm 2.71... A Sequence S[n] is believed to converge to a ...
199 views

### Approximation in LinePlot from NIntegrate

I am facing an approximation issue during a plot from numerical integration through NIntegrate. The code is: ...
1 vote
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### Is function MiniMaxApproximation equivalent to Remez algorithm?

I'm looking for function calculating polynomial of best approximation (in sense of uniform norm) to given function $f(x)$ on interval $[a,b]$. I know Remez algorithm doing this. In ...
1 vote
133 views

### What's the command for high approximation up to 50 digits?

I am trying to find the numerical value of $\displaystyle \sum_{n=1}^\infty \frac{e^{-n^2/\pi^2}}{n^2}$ up to 50 digits. I used ...
212 views

### Solving symbolically a trascendental equation containing an exponential

Is it possible to solve symbolically this equation for $x$: $$\exp \left(-x^2\right)=\frac{c_1}{\sqrt{c_2-c_3 x}}$$ Exp[-x^2] == c1/Sqrt[c2 - c3 x] $c_1$, $c_2$ ...
1 vote
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### approximating large numbers

I want to get the zeros of a function $f(w,a)$ with respect to $a$. Thats not the problem. But the problem is, that the zeros are very large numbers. And I want them to be displayed in a short ...
1 vote
160 views

### Homework from studies! - module computation of an approximating function

Polynomial approximation The aim of the task: to write a program in the form of a module in the Mathematica® machine code computation of an approximating function F (·) for an approximated ...
73 views

### Why do these two methods give different answers for this simple approximation?

I tried to find Padé approximant of the function below using two different methods, but the results were not equal. $f(x)=1+x+x^2+x^3+\cdots$ Method 1: Using the direct built in function of Padé ... 178 views

Does Mathematica generate multivariate or just two-variate Pade approximant? If so, what is the generating command?
130 views

### Setting Precision in For

How do you set the precision for a function where you substitute a number in a For loop? I mean I code something like this and I want Mathematica to set the precision for all the values ...
1 vote
67 views

### What Algorithm Does EconomizedRationalApproximation Use?

I'm very interested in Approximation Theory, especially with Continued Fractions and Rational Functions. I really like the approximations that Mathimatica gives with EconomizedRationalApproximation[]...
115 views

### Nested NIntegrate over a region: Numerical Integration not converging

I need to computed two double nested numerical integrals, of which one is defined over a specific region (e.g. a pentagon). I've tried to use a single NIntegrate with four variables, but the result is ...
115 views

### Series expansion of a function up to linear terms [duplicate]

I have the following: \[CapitalSigma] = r^2 + a^2 Cos[\[Theta]]^2; \[CapitalDelta] = r^2 - 2 M r + a^2 - k/3 r^2 (r^2 + a^2); grr = \[CapitalSigma]/\[CapitalDelta]; ...
150 views

### Inverse Functions

I'm new to Mathematica, so I fell sorry for posting relativily naive/dumb questions. I have these two functions that represent X coordinate distortion of an SLA 3D printer. ...
55 views

### Approximating giant polynomial expression

Suppose I have a giant polynomial expression analogous to $$F=a_1xX^6+a_2x^2X^5+a_3x^3X^4+a_4x^4X^3+a_5x^5X^2+a_6x^6X$$ and it is true that $X \gg x$. Let it be enough for me to approximate this ...
812 views

My Question is about two points Pade approximant From Mathematica References. I just find the Pade approximant for a real function in one point Example : ...
1 vote
134 views

### Function decomposition to Fourier series using first impulse function

I have periodic function with certain first impulse function and period value. My task is to decompose it to approximate Fourier series (k_max = 10) using Laplace transform of first impulse function: ...
1 vote
304 views

### how to transform a decimal into a radical equivalent with minimal error,and find a correct syntax?

I have been solving this equation x^x^x == 36 , Mathematica does not give me a solution by applying traditional methods , neither with ...
135 views

### Comparing the plots of two functions in number theory

Definition. For $x>1$, let $$R(x):=\sum_{n\ge1}\frac{\mu(n)}{n}\,\operatorname{li}(x^{1/n})$$ denote the Riemann prime counting function. If you are not familiar with the mathematical expressions ...
400 views

### Suggest an irrational number from decimal one

I want to know is there any function in Mathematica that suggests a simple irrational number combination for decimal one? For example, if I give 0.804738 then I get ...
57 views

### 3D plot using Table & FindRoot

I have two expressions involving terms $S_1$ and $S_2$, call the expressions $F1, F2$. I cannot solve $F_i=1$ for $S_i$ so instead I numerically approximate using ...
1 vote
228 views

### How to approximate the harmonic sum $\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$

How to approximate $$\sum_{n=1}^\infty\frac{{4n\choose 2n}\overline{H}_{2n}}{n 2^{4n}} ?$$ Where $\overline{H}_n=\sum_{k=1}^n \frac{(-1)^{k-1}}{k}$ is the skew harmonic number. The mathematica ...
94 views