Questions tagged [series-expansion]
Questions on dealing with series data and constructing power series expansions of functions.
953 questions
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Reducing a symbolic expression to only its lowest-order terms
Suppose I have an expression which is a collection of symbols and integers arbitrarily combined with Plus and Times. For example,...
- 165
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2
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117
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Approximately solving this equation among probabilities/LLRs symbolically
Consider three independent Bernoulli events $A, B, C$ with success probabilities $p, q$ and $r$ respectively. Let us define two more derived events $L$ and $M$ with probabilities $p_1$ and $p_2$ given ...
- 281
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Can series expansion variable be substituted with numeric value?
The documentation page for Series under the section Possible issues states that
"Numeric values cannot be substituted directly for the expansion variable in a ...
- 157k
5
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3
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241
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How to determine the order of poles of a symbolic expression in Mathematica?
Consider the following trigonometric sum in Mathematica:
...
- 954
2
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0
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84
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Error with series of spherical bessel SphericalBessel?
Below seems like some error in the spherical bessel series expansion around an arbitrary number a. All terms below should be equal. Except term1 is different from all the others!
...
- 606
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2
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Help with asymptotics on an interesting sum
I recently learned an interesting limit and was trying to understand the asymptotics. Unfortunately I'm getting nowhere.
Take ...
- 43
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44
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Defining multilinear function series expansion
I want to define an abstract multilinear function mlfunc in arbitrary arguments with the standard algebraic and analytic properties.
Implementing algebraic ...
- 181
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2
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220
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Finding asymptotes of a function defined by a relation of two variables
Based on this question, how does one analytically compute the asymptotes for the equation defined by:
$$(x+y+2)(x+y)^2 = x+9y-2 ?$$
I can easily plot the curve...
and can manipulate equation for ...
- 43.3k
0
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Inconsistent recurrence relation for Weierstrass sigma function double series between MathWorld and DLMF
There is a curious recurrence relation for double series of Weierstrass sigma function listed at DLMF defition 23.9.8
$$
a_{m,n} = 3(m+1) a_{m+1,n-1} + \frac{16}{3}(n+1) a_{m-2,n+1} - \frac{1}{3}(2m+...
- 694
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Help to try and make my code finish running. Series of incomplete elliptic integrals
I have the following code
...
- 231
0
votes
0
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96
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Result of Series inconsistent with requested order of expansion
Consider the following simple Series invocation,
Series[a*x^2, {x, 0, 1}]
In Mathematica 14.3 it returns
a*x^2+O[x]^3
This ...
- 43
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How to syntax products and append each result to a table?
I'm still trying to learn how to code the results of the LHS and RHS of this famous equation into a table:
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{A}$$
I asked this ...
- 181
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2
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How to output results of the sum, $\sum_{a=1}^2\sum_{b=1}^a\sum_{c=1}^b 2^a3^b 5^c$ into a list (table)?
I'm trying to write a code that can approximate the following formula,
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{A}$$
In this M.SE question I was convinced that $(\...
- 181
3
votes
5
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656
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How to approximate an implicit function using simple functions (e.g. polynomials)?
I am trying to approximate the following function using taylor series (to express $y$ as an explicit function of $x$ for $0.3<y<1$):
$$
x = a (1-y)^b + c \sinh(d (1-y))
$$
where $a$, $b$, $c$, ...
- 641
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2
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How to output each summand of $\sum_{n=1}^k \frac1n$ into a list?
From real analysis, I'm trying to learn more about this famous equation in this post of Mathematics.SE:
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{1}$$
I won't ask ...
- 181