Indeterminate moment problems related to birth and death processes with quartic rates (Q1772333)

\textit{G. Valent} in [SIAM J. Math. Anal. 25, 749--775 (1994; Zbl 0796.33004)] considered as an example the birth and death process with quartic rates \(\lambda_n=(4n+4c+1)(4n+4c+2)^2(4n+4c+3)\) and \(\mu_n=(4n+4c-1)(4n+4c)^2(4n+4c+1)(1-\delta_{n,0})\). In the paper under review the author considers an indeterminate symmetric moment problem related to the birth and death process with \(c=\frac14\) and compares it with the case \(c=0\) [this case was studied by \textit{C. Berg} and \textit{G. Valent} in Methods Appl. Anal. 1, No.~2, 169--209 (1994; Zbl 0966.44500)]. He presents Nevanlinna matrices. The entire functions \(B\) and \(D\) are expressed in terms of the trigonometric functions of order 4. He concludes the paper with several examples of symmetric and nonsymmetric solutions to the moment problems.