Application of Stieltjes Theory for $S$-Fractions to Birth and Death Processes. Bordes, G. & Roehner, B. Advances in Applied Probability, 15(3):507–530, September, 1983.
Application of Stieltjes Theory for $S$-Fractions to Birth and Death Processes [link]Paper  doi  bibtex   
@Article{Bordes:1983:AST,
  author =       "G. Bordes and B. Roehner",
  title =        "Application of {Stieltjes} Theory for {$S$}-Fractions
                 to Birth and Death Processes",
  journal =      j-ADV-APPL-PROB,
  volume =       "15",
  number =       "3",
  pages =        "507--530",
  month =        sep,
  year =         "1983",
  CODEN =        "AAPBBD",
  DOI =          "https://doi.org/10.2307/1426617",
  ISSN =         "0001-8678 (print), 1475-6064 (electronic)",
  ISSN-L =       "0001-8678",
  bibdate =      "Sat May 3 07:41:38 MDT 2014",
  bibsource =    "http://www.jstor.org/stable/i262259;
                 http://www.math.utah.edu/pub/tex/bib/advapplprob.bib",
  URL =          "http://www.jstor.org/stable/1426617",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Appl. Probab.",
  fjournal =     "Advances in Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00018678.html",
}

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