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An adjacent question was posted to math stack exchange, but had no answer, so hopefully Math Overflow can provide more insight.
The Kampé de Fériet function seems to be the most well known 2 variable hypergeometric or Mellin Barnes type function with an adjustable amount of parameters (like $a_A$):...

Let $p,q$ be two distinct odd primes and, as usual, let $\Phi_{p}(x)$ the $p$-th cyclotomic polynomial. The prime divisors of this polynomial are, up to one exception, exactly those $1 \mod p$. In principle, there should be no similar restriction $\mod...

In Higher Algebra, Remark 1.2.4.3, Lurie associates to a simplicial object$$X_\bullet:\mathrm{N}_\bullet(\boldsymbol{\Delta})^{\operatorname{op}}\to \mathcal{C}$$in a stable $\infty$-category $\mathcal{C}$ a filtered object whose graded pieces are denoted...

I am wondering whether, if a triangulated category $\mathcal{D}$ has a full strong exceptional collection (infinite), it is triangle-equivalent to the bounded derived category of finitely generated modules over an algebra?