[{"language":[{"iso":"eng"}],"department":[{"_id":"17982"}],"first_author":"Andrae, Dirk","publication_identifier":{"issn":["0953-4075"],"eissn":["1361-6455"]},"type":"journal_article","citation":{"mla":"Andrae, Dirk. “Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom”. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS* 30.20 (1997): 4435-4451.","frontiers":"Andrae, D. (1997). Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS* 30, 4435-4451.","angewandte-chemie":"D. Andrae, “Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom”, *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*, **1997**, *30*, 4435-4451.","ieee":" D. Andrae, “Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom”, *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*, vol. 30, 1997, pp. 4435-4451.","apa_indent":"Andrae, D. (1997). Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*, *30*(20), 4435-4451. doi:10.1088/0953-4075/30/20/008

","dgps":"Andrae, D. (1997). Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*, *30*(20), 4435-4451. IOP PUBLISHING LTD. doi:10.1088/0953-4075/30/20/008.

","apa":"Andrae, D. (1997). Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*, *30*(20), 4435-4451. doi:10.1088/0953-4075/30/20/008","chicago":"Andrae, Dirk. 1997. “Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom”. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS* 30 (20): 4435-4451.

","harvard1":"Andrae, D., 1997. Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*, 30(20), p 4435-4451.","aps":" D. Andrae, Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom, JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS **30**, 4435 (1997).","ama":"Andrae D. Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*. 1997;30(20):4435-4451.","lncs":" Andrae, D.: Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom. JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS. 30, 4435-4451 (1997).","bio1":"Andrae D (1997)

Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom.

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS 30(20): 4435-4451.","default":"Andrae D (1997)

*JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS* 30(20): 4435-4451.","wels":"Andrae, D. (1997): Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom *JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS*,30:(20): 4435-4451."},"external_id":{"isi":["A1997YD77800008"]},"quality_controlled":"1","abstract":[{"text":"An algorithm for the recursive evaluation of expectation values (r(k)) for a given state of the relativistic one-electron atom with a point-like nucleus of charge number Z is proposed. In contrast to previous approaches, the present algorithm is based on only a single recurrence relation, which is a recurrence relation for a special type of generalized hypergeometric F-3(2) series. Two sequences of values of such 3 F-2 series are generated. Finally, the members of these two sequences are assembled to yield the expectation values. The algorithm can be considered as a relativistic analogue of the Kramers-Pasternack recursion for expectation values (r(k)) for states of the non-relativistic hydrogen-like atom. As an application closed-form expressions for (r(k)), -6 less than or equal to k less than or equal to 5, were derived. In addition, numerical values for (r(k)) are given for some representative states of one-electron atoms with Z = 1, 80 and 137.","lang":"eng"}],"title":"Recursive evaluation of expectation values (r(k)) for arbitrary states of the relativistic one-electron atom","publication":"JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS","intvolume":" 30","doi":"10.1088/0953-4075/30/20/008","year":"1997","accept":"1","_id":"1627292","status":"public","isi":"1","article_type":"original","date_submitted":"2010-12-07T16:48:27Z","volume":"30","page":"4435-4451","publication_status":"published","author":[{"id":"20327","full_name":"Andrae, Dirk","first_name":"Dirk","last_name":"Andrae","autoren_ansetzung":["Andrae, Dirk","Andrae","Dirk Andrae","Andrae, D","Andrae, D.","D Andrae","D. Andrae"]}],"date_created":"2010-04-28T13:22:13Z","id":"1627292","publisher":"IOP PUBLISHING LTD","issue":"20","date_updated":"2018-07-24T12:57:50Z"}]