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Nov
27
comment Replacing functions
This question is quite puzzling, because neither Sin[x] nor x can reliably be construed as "functions." Shouldn't the first example return Sin[x][x]-3? If that seems silly, suppose Sin were a function that returns a function, as in sin[x_]:=Function[{y},y+x]. Now both sin[x][x] and sin[x] make sense, but only the former conforms to the problem statement in the first line (and evaluates to x+x, by the way).
Nov
27
awarded  Nice Answer
Nov
27
comment Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
@VF1 What specific expression are you suggesting?
Nov
26
comment Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
Re the second part of the question: there are many more than five solutions, no matter how flexible you are in rewriting them. E.g., $34(-5\times 6 + 89)+2$ or $34(5/(6/(8\times 9))-1)+2$.
Nov
26
revised Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
added 1038 characters in body
Nov
26
answered Are table headings functional?
Nov
26
revised Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
added 231 characters in body
Nov
26
revised Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
added 3099 characters in body
Nov
25
comment Checking if a point is in a convex 3D polyhedron
Generating convex polyhedron from face planes is closely related because when the planes' normal vectors are consistently oriented, they provide a simple mechanism for determining whether points are inside or outside (as illustrated, for instance, in the code in my answer in that thread: see the argument to the RegionPlot3D example there).
Nov
25
revised Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
added 5157 characters in body
Nov
25
comment Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
@Rojo Many thanks for making that observation. It appears something very strange is happening with ParallelMap: it frequently "loses" about 95% of the solutions compared to those found by Map. I will rewrite this answer to avoid that problem and to include better explanations of what exactly is being done.
Nov
23
answered Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
Nov
23
reviewed Close Placing a ContourPlot under a Plot3D
Nov
22
comment Dashed line with alternating colored dashes
Filling is optional...
Nov
22
answered Dashed line with alternating colored dashes
Nov
21
comment Multi-Factorial and Series with Triple-factorial terms
+1. If you follow the strategy outlined in my answer of first simplifying the coefficients, there won't be any problem: a[j_] := Evaluate [ FullSimplify[MultiFactorial[3 j, 3]/MultiFactorial[3 j + 1, 3], Assumptions -> j \[Element] Integers]] re-expresses the sum in terms of Gamma functions and you're all set.
Nov
21
comment Multi-Factorial and Series with Triple-factorial terms
@J.M. Thank you for looking at this! I made a really stupid mistake by using the wrong definition for a. This requires a different approach, which I have incorporated in an edited version. The new approach is a little weaker because it's not fully automatic and elementary, but it may still be of interest in showing how to discover useful formulas for recursively defined functions and how to prove them correct once they have been found.
Nov
21
revised Multi-Factorial and Series with Triple-factorial terms
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Nov
21
comment Multi-Factorial and Series with Triple-factorial terms
Replacing $3$ by $k$ gives the solution $_2F_1\left[1,1,1+\frac{1}{k},x\right]$. Applying FunctionExpand for the case $k=3$ and simplifying yields $-\frac{2 \sqrt{3} \text{ArcTan}\left[1-\frac{x^{1/3}}{2 (1-x)^{1/3}},-\frac{\sqrt{3} x^{1/3}}{2 (1-x)^{1/3}}\right]-2 \text{Log}\left[1+\frac{x^{1/3}}{(1-x)^{1/3}}\right]+\text{Log}\left[1+\frac{x^{‌​2/3}-(-(-1+x) x)^{1/3}}{(1-x)^{2/3}}\right]}{6 (1-x)^{2/3} x^{1/3}}$, showing the connection with ArcTan and Log.
Nov
21
answered Multi-Factorial and Series with Triple-factorial terms