# Tag Info

### 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 ...
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### 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 ...
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### 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: ...

### 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 ...

### How do I get other representations of the Gamma function?

Use Entity["MathematicalFunction", "Gamma"] ...
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### 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 ...
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### 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, ...
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### 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 ...