I think (integration) might be suitable for those two question too. But at least for the other 14 questions, merging into into (integration) won't change anything else, only remove the (gradshteyn-ryzhik) tag.
Preamble
I've stumbled upon (a particular variant of) Fibonacci polynomials in my work, defined by
$$
F_k(x) = \begin{cases} \qquad\qquad 1, & k=1 \\ \qquad\qquad 1, & k=2 \\ F_{k-1}(x) + x\!\; F_{k-2}(x), & k > 2 \end{cases}
$$
giving rise to a sequence of polynomials starting with
$$\begin{ali...
Given the polynomial
$$p(x,y)=2y^4x+y^3x^2-2y^2x^3-y^5-yx^4+2y$$
how would one prove that its positive values of $p$ (for $x=1,2,...,y=1,2...$) coincide with the Fibonacci numbers?
Tried something like $p(x-1, y-2)$ or $p(x-2, y-2) + p(x-1, y-1)$. But it didn't work, of course.
I've figured ...
Proposal: Keep tag gradshteyn-ryzhik for questions related to formulas found specifically in the book Table of Integrals, Series, and Products.
There are currently about 120 questions about formulas found in the above book, so I have tagged some of these questions with gradshteyn-ryzhik.
Altho...
Or is it enough to mention in the comments that the tag has been removed?
Given the polynomial
$$p(x,y)=2y^4x+y^3x^2-2y^2x^3-y^5-yx^4+2y$$
how would one prove that its positive values of $p$ (for $x=1,2,...,y=1,2...$) coincide with the Fibonacci numbers?
Tried something like $p(x-1, y-2)$ or $p(x-2, y-2) + p(x-1, y-1)$. But it didn't work, of course.
I've figured ...
Proposal: Keep tag gradshteyn-ryzhik for questions related to formulas found specifically in the book Table of Integrals, Series, and Products.
There are currently about 120 questions about formulas found in the above book, so I have tagged some of these questions with gradshteyn-ryzhik.
Altho...
