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Denis Serre
Denis Serre
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In a calculation of some momenta of random matrices (GOE), I encounter a functional equation, in the form of a second-order recursion, $$L(s+1)=L(s)+2s(2s+1)L(s+1).$$$$L(s+1)=L(s)+2s(2s+1)L(s-1).$$ Is it familiar to someone ? Is there an explicit formula for the solutions ? By explicit, I mean in terms of the Gamma function for instance.

Just in case, I am interested in the solution generated by $L(0)=1$ and $L(1)=-\frac18$ .

In a calculation of some momenta of random matrices (GOE), I encounter a functional equation, in the form of a second-order recursion, $$L(s+1)=L(s)+2s(2s+1)L(s+1).$$ Is it familiar to someone ? Is there an explicit formula for the solutions ? By explicit, I mean in terms of the Gamma function for instance.

Just in case, I am interested in the solution generated by $L(0)=1$ and $L(1)=-\frac18$ .

In a calculation of some momenta of random matrices (GOE), I encounter a functional equation, in the form of a second-order recursion, $$L(s+1)=L(s)+2s(2s+1)L(s-1).$$ Is it familiar to someone ? Is there an explicit formula for the solutions ? By explicit, I mean in terms of the Gamma function for instance.

Just in case, I am interested in the solution generated by $L(0)=1$ and $L(1)=-\frac18$ .

Source Link
Denis Serre
Denis Serre
  • 52.3k
  • 10
  • 146
  • 300

A second-order recursion (functional equation)

In a calculation of some momenta of random matrices (GOE), I encounter a functional equation, in the form of a second-order recursion, $$L(s+1)=L(s)+2s(2s+1)L(s+1).$$ Is it familiar to someone ? Is there an explicit formula for the solutions ? By explicit, I mean in terms of the Gamma function for instance.

Just in case, I am interested in the solution generated by $L(0)=1$ and $L(1)=-\frac18$ .