2015-01-142015-01-1420131815-0659http://hdl.handle.net/11441/17467The use of spectral methods to study birth-and-death processes was pioneered by S. Karlin and J. McGregor. Their expression for the transition probabilities was made explicit by them in a few cases. Here we complete their analysis and indicate a few applications of their very powerful method.engAtribución-NoComercial-SinDerivadas 4.0 Españahttp://creativecommons.org/licenses/by-nc-nd/4.0/Birth-and-death processesSpectral measureinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.3842/SIGMA.2013.020https://idus.us.es/xmlui/handle/11441/17467