For a complex differential equations with meromorphic coefficients of finite (p,q)-order, it's well known that if f is a solution then (p+1,q)- order of f is less than max{(p,q)-order of coefficients}, and some time with certain conditions we can be sur that (p+1,q)- order of f is equal to max{(p,q)-order of coefficients},
in some articles, the authors used the meromorphic version of Wiman-Valiron theorem to estimate some logarithmic derivativse, and this last theorem was used under the condition that (p,q)-order of f doesn't vanish.
So, the main question here (It might be so simple to be asked) is as follows :
Can we find a solution of (p+1,q)-order =0 to ODE with finite (p,q)-order meromorphic functions ?
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