Questions tagged [series-expansion]
Questions on dealing with series data and constructing power series expansions of functions.
946 questions
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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 ...
- 43k
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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
$$
a_{m,n} = 3(m+1) a_{m+1,n-1} + \frac{16}{3}(n+1) a_{m-2,n+1} - \frac{1}{3}(2m+...
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Help to try and make my code finish running. Series of incomplete elliptic integrals
I have the following code
...
- 221
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Result of Series inconsistent with requested order of expansion
Consider the following simple Series invocation,
Series[a*x^2, {x, 0, 1}]
In Mathematica 14.3 it returns
a*x^2+O[x]^3
This ...
- 43
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How to syntax products and append each result to a table?
I'm still trying to learn how to code the results of the LHS and RHS of this famous equation into a table:
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{A}$$
I asked this ...
- 171
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How to output results of the sum, $\sum_{a=1}^2\sum_{b=1}^a\sum_{c=1}^b 2^a3^b 5^c$ into a list (table)?
I'm trying to write a code that can approximate the following formula,
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{A}$$
In this M.SE question I was convinced that $(\...
- 171
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How to approximate an implicit function using simple functions (e.g. polynomials)?
I am trying to approximate the following function using taylor series (to express $y$ as an explicit function of $x$ for $0.3<y<1$):
$$
x = a (1-y)^b + c \sinh(d (1-y))
$$
where $a$, $b$, $c$, ...
- 589
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2
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How to output each summand of $\sum_{n=1}^k \frac1n$ into a list?
From real analysis, I'm trying to learn more about this famous equation in this post of Mathematics.SE:
$$\sum_{n=1}^\infty \frac1n=\prod_{i=1}^\infty\frac{1}{1-\frac{1}{p_i}}\tag{1}$$
I won't ask ...
- 171
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Evaluating series with functions as coefficients results in Power::indet
Mathematica seems to have a problem evaluating a series in which the coefficients are functions. Here is an example.
...
- 41
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Unexpected behavior of `Series` for version 14.3?
Bug introduced in 14.3 or earlier and persisting through 14.3.0 or later
Consider the simple example
$Version
Series[\[Chi],{\[Chi],0,0}]
Before version 14.3, the ...
- 3,467
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1
answer
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Find real and imaginary parts of a complex series
I have the following complex series:
$$S=\sum _{n=0}^{\infty} \frac{3\,a^n }{(2n+1) (2n+3) \left(1+\dfrac{b}{x+iy }\right)^{2n+1}}\left(\frac{t}{x+i y}\right)^{2n}$$
where $a,b,t$ are real.
This ...
- 1,038
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Series expansion involving incomplete Beta function
I am trying to expand the following around u=1/2.
...
- 1,957
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2
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Expanding the HypergeometricPFQ function gives complex values
I have a function
HypergeometricPFQ[{}, {2, 2}, -Log[n]]
which for real n > 0 gives a real values, as can be seen on the ...
- 3,471
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Optimizing my code so it runs faster, Series function
I am trying to compute expansions of some fairly long expressions using the built in function Series in Mathematica, and I was wondering if there is anything I can do in order to make the code run ...
- 221
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Series expansion from NIntegrate
I have a very nasty integrand
$$A(q,\Omega,k,\beta,y,x)= \int \mathrm{d}k \, \mathrm{d}x \, \mathrm{integrand_A}$$
where $\beta,y$ are numbers, and I integrate over $k$ and $x$ so at the end I only ...
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