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- W3068794293 abstract "For any $A(z),B(z),C(z)inmathbb{C}z$, we study the zero distribution of a table of polynomials ${P{m,n}(z)}{m,ninmathbb{N}_0}$ satisfying the recurrence relation $$ P{m,n}(z)=A(z)P{m-1,n}(z)+B(z)P{m,n-1}(z)+C(z)P{m-1,n-1}(z) $$ with the initial conditions $P{0,0}(z)=1$ and $P{-m,-n}(z)=0$ for all $m,ninmathbb{N}$. We show that the zeros of $P_{m,n}(z)$ lie on a curve whose equation is given explicitly in terms of $A(z)$, $B(z)$, and $C(z)$. We also study the zero distribution of a case with a general initial condition." @default.
- W3068794293 created "2020-08-24" @default.
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- W3068794293 date "2022-05-12" @default.
- W3068794293 modified "2023-09-25" @default.
- W3068794293 title "Zeros of a table of polynomials satisfying a four-term contiguous relation" @default.
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- W3068794293 doi "https://doi.org/10.4171/zaa/1698" @default.
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