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}{...
6 votes

Evaluate using Mathematica or otherwise the value of $f'(0)$

Let's define ...
  • 55.8k
6 votes
Accepted

Intersection points of two-variable polynomials

We define: ...
  • 55.8k
5 votes
Accepted

Solving analytical integral

If you add assumptions that variables are positive, then ...
  • 139k
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!
4 votes

Intersection points of two-variable polynomials

...
  • 41k
4 votes
Accepted

Assume asymptotic value in a limit?

ClearAll[a, F, r, t, x] Use TagSet to define UpValues for ...
  • 139k
3 votes

Evaluate using Mathematica or otherwise the value of $f'(0)$

...
  • 139k
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. ...
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 ...

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