9
votes
Evaluate using Mathematica or otherwise the value of $f'(0)$
From definition of HypergeometricPFQ as Series representations we have:
$\underset{a\to 0}{\text{lim}}\frac{\partial }{\partial a}\, _3F_2\left(\frac{1}{2},\frac{1}{...
- 12.4k
6
votes
6
votes
Accepted
5
votes
Accepted
4
votes
Accepted
Series expansion using binomial theorem in Mathematica
$Version
(* "13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023)" *)
Clear["Global`*"]
f[x_] := (1 - a/x)^(1/3)
Do a series expansion about <...
- 139k
4
votes
Series expansion using binomial theorem in Mathematica
You are almost there. Try the following:
Series[(1 - (a/x))^(1/3), {a, 0, 2}] // Normal
(* 1 - a^2/(9 x^2) - a/(3 x) *)
Have fun!
- 37k
4
votes
4
votes
Accepted
Assume asymptotic value in a limit?
ClearAll[a, F, r, t, x]
Use TagSet to define UpValues for ...
- 139k
3
votes
2
votes
Accepted
Analytical Solution in Generalized Heat Equation
just to add more to the comment, to help show why this is hard to solve analytically using separation of variables.
To solve using separation of variables we must be able to find the eigenvalues of ...
- 127k
2
votes
Intersection points of two-variable polynomials
Factoring shows they contain common factors.
...
- 57.3k
2
votes
Evaluate using Mathematica or otherwise the value of $f'(0)$
Mathematica evaluates a closed form as a ConditionalExpression
Limit[(f[a] - f[0])/a, a -> 0]
which is probably not useful because it contains unevaluated ...
- 42.9k
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