12 votes

Using Mathematica to derive analytic form of single variable function

If one makes a table of the first few values of $n$, then a pattern becomes evident: Table[{n, f[n]}, {n, 3, 8}] // TableForm One can see that the leading term is ...
user avatar
  • 34.8k
10 votes
Accepted

How can I calculate the sum of this series?

Exponentiation followed by logarithm works, really fast: Log@Product[1 + 1/n^2, {n, 1, Infinity}] // AbsoluteTiming (* {0.139728, Log[Sinh[π]/π]} *) Internal ...
user avatar
  • 220k
9 votes
Accepted

Get rid of a certain variable in a fraction's numerator

Try this: PolQuotient[num_, den_, var_] := PolynomialQuotient[num, den, var] + 1/den*PolynomialRemainder[num, den, var] Test: ...
user avatar
9 votes

Solving quintic in radicals

I reproduced the algorithm from this post and I tried to use it on your example: An Easy Way To Solve The Solvable Quintic Using Two Sextics. As mentioned in the article, for the quintic equation: $$a ...
user avatar
  • 3,696
9 votes
Accepted

How do I get other representations of the Gamma function?

There is MathematicalFunctionData which can be exploited to get various representations of the Euler Gamma function. As a ...
user avatar
  • 54.4k
9 votes

Making algebraic substitutions with approximations

You could use Series[c/(a^2 - a*b), {a, Infinity, 4}] which yields
user avatar
  • 5,308
8 votes

Integration Bug?

EDIT: The evaluation error pointed out in the OP has been accepted as a bug. This bug is most probably a problem in the kernel, and will be investigated carefully by Wolfram's expert team. ...
user avatar
8 votes
Accepted

the Bessel function Integration

$$\int_k^1 \ln (r) (J_0(a r)+b Y_0(a r)) \, dr=\int_k^1 \ln (r) J_0(a r) \, dr+\int_k^1 \ln (r) b Y_0(a r) \, dr$$ Mathematica have problems to compute the second define integral. One way is: ...
user avatar
7 votes

Analogue for Maple's dchange - change of variables in differential expressions

2022 Update: Included in Mathematica 13.1 As pointed out by xzczd in his question update, seven years later, finally Mathematica 13.1 introduced the new function DSolveChangeVariables which ...
user avatar
  • 434
7 votes

How do I get other representations of the Gamma function?

Use Entity["MathematicalFunction", "Gamma"] ...
user avatar
  • 123k
7 votes
Accepted

Zero result from a positive integral

Split the integration range from -Infinity to 0 and from 0 to Infinity. Add the two Rootsums and convert the result to radicals, then help Mathematica simplify the result. You will find ...
user avatar
  • 2,664
7 votes
Accepted

Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder

This post contains several code blocks, you can copy them easily with the help of functions here. It's not too surprising to see DSolve failing on the problem, ...
user avatar
  • 54.2k
7 votes
Accepted

How to achieve the transformation using DSolveChangeVariables introduced in Mathematica 13.1?

The problem can be solved with new-in-13.1 DSolveChangeVariables of course. If you read the document carefully, you'll notice the correct syntax should be ...
user avatar
  • 54.2k
7 votes
Accepted

Why Integrate gives warning "Internal precision limit $MaxExtraPrecision = 50. reached" when working on purely symbolic expression?

According to the stack trace in the N::meprec error message, it is from Sign[2 Log[2] - Log[4]], which is called when ...
user avatar
  • 220k
6 votes

DSolve not finding solution I expected

In V13.1, the new DSolve option IncludeSingularSolutions -> True yields the sought-after solution: ...
user avatar
  • 220k
6 votes
Accepted

Solving equations with symbolic variables

...
user avatar
  • 123k
6 votes

How can I calculate the sum of this series?

It's a backslide. v9.0.1 handles the problem without difficulty: Please report this to WRI. One possible work-around for higher version (somewhat opportunistic): ...
user avatar
  • 54.2k
6 votes

Difficulty evaluating integral with Boole

It is enough to use a single Integrate and to set Integrationpart x outer most: ...
user avatar
6 votes
Accepted

Introduce formal symbols indexed by natural numbers

It is often useful to avoid Subscript, Superscript, and Subsuperscript and instead to just ...
user avatar
  • 123k
6 votes
Accepted

Equating coefficients of two expressions

Another way with SolveAlways ...
user avatar
  • 16.5k
6 votes
Accepted

Simplifying expressions with nested square roots

As kindly pointed out by JimB in the comments, it turns out that the function I needed was given by Carl Woll in this answer: ...
user avatar
  • 385
6 votes
Accepted

Making algebraic substitutions with approximations

Using Asymptotic: Asymptotic[ (c/(a^2 - a b)), {b, 0, 1}] (*c/a^2*) Using Series and ...
user avatar
5 votes
Accepted

How to solve that logarithmic equation?

Not foolproof, but RootApproximant works for this case: ...
user avatar
  • 124k
5 votes
Accepted

How to handle excluded values in a summation or product in Mathematica

I assume you are asking how to exclude a single value from summation, i.e. the $i \ne j$ part in your $\sum_{i=0, i\ne j}^n$ example. You can simply use a conditional, such as ...
user avatar
  • 227k
5 votes
Accepted

Minors of a symbolic matrix

Minors does indeed work on symbolic matrices. However, the position of elements might be different than usual. Read the reference page for ...
user avatar
  • 7,522
5 votes

Reduce the number of equations

You can find variables to take as parameters by computing a Groebner basis after converting from equations to polynomials. The first polynomial will have seven variables, and we'll choose the six with ...
user avatar
5 votes

Three dimensional Laplacian insulated on lateral faces and convectively exposed on transverse faces (updated)

We can solve this problem with using method explained in my answer here and in my paper attached to this post. We solve in the unit cube system of equations ...
user avatar
  • 34.7k
5 votes

How more effectively solve problems with "FindInstance" when number of variables is significantly greater then number of equations

If number of variables is greater than the number of equations on might look for a minimum solution (similar to PseudoInverse for linear problems): Similar to @...
user avatar
5 votes

Transforming implicit solutions of an ODE involving InverseFunction to an explicit form

Mathematica cannot get rid of InverseFunction in this case at least up to version 13. If $s^2(t)$ is a cubic or quartic polynomial in $t$ and $r(s,t)$ is a rational ...
user avatar
  • 54.4k
5 votes

How can I calculate the sum of this series?

Do it for a bunch of values Table[Sum[Log[1 + 1/n^2], {n, 1, xx}], {xx, 1, 17}] // FullSimplify ...
user avatar
  • 4,153

Only top scored, non community-wiki answers of a minimum length are eligible