Funzioni di Bickley-Naylor

Le funzioni di Bickley-Naylor $\mathrm {Ki} _{n}(x)$ , dove $n\in \mathbb {N}$ e $x\in \mathbb {R}$ sono definite come:

\mathrm {Ki} _{n}(x)=\int _{0}^{\infty }{\frac {e^{-x\cosh u}}{\cosh ^{n}u}}\,du,

dove $cosh$ è la funzione coseno iperbolico.

Proprietà

Si ha:

{\frac {d}{dx}}\mathrm {Ki} _{n}(x)=-\mathrm {Ki} _{n-1}(x).

Per $n=0$ ,

\mathrm {Ki} _{0}(x)=\mathrm {K} _{0}(x)

dove $\mathrm {K} _{0}$ è una funzione di Bessel modificata.

Per $n=1$

\mathrm {Ki} _{1}(x)=\int _{x}^{\infty }\mathrm {K} _{0}(t)\,dt.

La funzione $\mathrm {Ki} _{1}(x)$ è anche collegata con l'integrale di Sievert:

\int _{0}^{\frac {\pi }{2}}d\phi e^{-x/\cos \phi }=\mathrm {Ki} _{1}(x).

Più generalmente,

\mathrm {Ki} _{n}(x)=\int _{0}^{\frac {\pi }{2}}d\phi \cos ^{n-1}\phi e^{-x/\cos \phi }

Applicazioni

Le funzioni di Bickley-Naylor si incontrano in problemi di diffusione dei neutroni e problemi di convezione.

Bibliografia

(EN) W. G. Bickley, Some solutions of the problem of forced convection, in Philosophical Magazine, vol. 20, n. 132, Londraid= DOI: 10.1080/14786443508561482, Taylor & Francis, 1935, pp. 322-343.
(EN) W. G. Bickley, John Nayler, A short table of the functions Ki_n(x), from n=1 to n=16, in Philosophical Magazine, vol. 20, n. 132, Londra, Taylor & Francis, 1935, pp. 343-347, DOI: 10.1080/14786443508561483.
(EN) J. M. Blair, C. A. Edwards; J. H. Johnson, Rational Chebyshev Approximations for the Bickley Functions Ki_n(X), in Mathematics of Computation, vol. 32, n. 143, American Mathematical Society, luglio 1978, pp. 876-886, JSTOR 2006492.

Collegamenti esterni

BICKLEY-NAYLOR FUNCTIONS Ki_n(x) AND THEIR PROPERTIES (PDF), su www2.ogu.edu.tr. URL consultato il 21 gennaio 2012 (archiviato dall'url originale il 16 febbraio 2010).
(EN) Digital Library of Mathematical Functions, Fractional Integrals, su dlmf.nist.gov. URL consultato l'11 novembre 2012.

Read other articles:

Enrico Berlinguer

Enrico Berlinguer Sekretaris jenderal Partai Komunis ItaliaMasa jabatan17 Maret 1972 – 11 Juni 1984PresidenLuigi Longo PendahuluLuigi LongoPenggantiAlessandro NattaSekretaris Federasi Pemuda Komunis ItaliaMasa jabatan12 April 1949 – 14 Maret 1956 PendahuluAgostino NovellaPenggantiRenzo TrivelliAnggota Kamar DeputiMasa jabatan5 Juni 1968 – 11 Juni 1984Daerah pemilihanRoma Informasi pribadiLahir25 Mei 1922Sassari, Kerajaan ItaliaMeninggal11 Juni 1984(1984-06-11)...

Mehriban Aliyeva

Mehriban Aliyeva(2023) Nama dalam bahasa asli(az) Mehriban Arif qızı Əliyeva BiografiKelahiran26 Agustus 1964 (59 tahun)Baku 1a Wakil Presiden Azerbaijan 21 Februari 2017 – First Lady of Azerbaijan (en) 31 Oktober 2003 – Member of the National Assembly of Azerbaijan (en) Daerah pemilihan: Q12835062 Data pribadiAgamaIslam PendidikanI.M. Sechenov First Moscow State Medical University (en) KegiatanPekerjaanOphthalmologist (en), ...

Egidio Salvi

Egidio Salvi Salvi (a destra) premiato dal presidente Sergio Saleri al Brescia Nazionalità Italia Calcio Ruolo Allenatore (ex centrocampista, attaccante) Termine carriera 1981 - giocatore 1998 - allenatore Carriera Giovanili Brescia Squadre di club1 1963-1968 Brescia111 (8)1968-1969 Napoli16 (0)1969-1980 Brescia286 (19)1980-1981 Romanese27 (5) Carriera da allenatore 1982-2008 BresciaGiov. Naz.1998 Brescia[1]2008-2011 BresciaVice Primave...

Dennis Srbeny

Questa voce sull'argomento calciatori tedeschi è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Dennis Srbeny Nazionalità Germania Altezza 190 cm Peso 83 kg Calcio Ruolo Attaccante Squadra Greuther Fürth Carriera Giovanili 2008-2011 TeBe Berlino2011-2013 Hertha Zehlendorf Squadre di club1 2013-2015 Hansa Rostock II34 (13)2014-2015 Hansa Rostock20 (1)2015-2017 BFC D...

Galangal

Member of the ginger family For the rhizome-bearing plant sometimes known as galingale, see Cyperus longus. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Galangal – news · newspapers · books · scholar · JSTOR (February 2010) (Learn how and when to remove this message) Kaempferia galanga Lesser galangal (Al...

Washington-Lee High School

Washington-Lee High SchoolInformasiDidirikan1925Jenishigh schoolKepala SekolahGregg RobertsonAlamatKampusSuburbanMoto[1] Washington-Lee High School (W-L) adalah salah satu dari tiga sekolah umum di distrik Arlington Public Schools, Arlington, Virginia, mencakup kelas dari 9–12, selain Yorktown High School, juga di Arlington utara, dan Wakefield High School Arlington Selatan. Secara konsisten sekolah ini memiliki posisi tinggi di peringkat nasional untuk persiapan kuliah, dengan...

Martha MacIsaac

Martha MacIsaacLahir11 Oktober 1984 (umur 39)Charlottetown, Prince Edward Island, CanadaPekerjaanActressTahun aktif1998–presentSuami/istriTorre Catalano (m. 2010; c. 2015) Martha MacIsaac (lahir 11 Oktober 1984) adalah seorang aktris berkebangsaan Kanada. Ia telah mengisi berbagai film seperti Superbad (2007), The Last House on the Left (2009), Dead Before Dawn (2012), dan paling terkenal, Battle of the Sexes (2017). Ia juga ber...

Quiz

Form of game or mind sport in which the players attempt to answer questions correctly For other uses, see Quiz (disambiguation). This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Quiz – news · newspapers · books · scholar · JSTOR (April 2008) (Learn how and when to remove this message) A printed quiz on health...

After Hegemony

After Hegemony (judul lengkap: After Hegemony: Cooperation and Discord in the World Political Economy)[1] adalah buku karya Robert Keohane. Buku ini merupakan teks utama dalam pendidikan hubungan internasional mazhab neoliberal. Referensi ^ http://press.princeton.edu/titles/1322.html lbsTeori hubungan internasionalRealisme Realisme neoklasik Neorealisme (realisme struktural) Realisme klasik Realisme ofensif Realisme defensif Realisme liberal (Mazhab Inggris) Keunggulan relatif Keunggu...

جامعة اللغونة

جامعة اللغونة معلومات التأسيس 1927 الموقع الجغرافي إحداثيات 28°28′54″N 16°19′01″W / 28.481761111111°N 16.317047222222°W / 28.481761111111; -16.317047222222 المكان سان كريستوبال دي لا لاغونا البلد إسبانيا إحصاءات عضوية رابطة الجامعات الأوروبية[1] الموقع الموقع الرسمي، ...

256th Infantry Division

256th Infantry Division256. Infanterie-DivisionDivision InsigniaActive26 August 1939 - 26 June 1944September 1944 - May 1945Country Nazi GermanyBranchArmyTypeInfantrySizeDivisionEngagementsWorld War IIInsigniaIdentificationsymbolIdentificationsymbolIdentificationsymbolIdentificationsymbolIdentificationsymbolMilitary unit The 256th Infantry Division (256. Infanterie-Division) was a German infantry division in World War II. They formed on August 1939 as part of the 4. Welle (wave). The div...

Liao Chengzhi

Chinese politician (1908–1983) Liao ChengzhiLiao in the late 1940s[1]Director of the Overseas Chinese Affairs Office Personal detailsBorn(1908-09-25)25 September 1908Okubo, Tokyo, JapanDied10 June 1983(1983-06-10) (aged 74)Peking Union Medical College Hospital, Beijing, ChinaPolitical partyChinese Communist PartyRelationsLiao Zhongkai (father)He Xiangning (mother)Liao Mengxing (sister)ChildrenLiao Hui In this Chinese name, the family name is Liao. Liao Chengzhi (Chinese: �...

History of the Jews in Zimbabwe

The location of Zimbabwe in Africa Ethnic group Zimbabwean JewsTotal population200LanguagesEnglish, Hebrew, YiddishReligionJudaismRelated ethnic groupsSouth African Jews Part of a series onJews and Judaism Etymology Who is a Jew? Religion God in Judaism (names) Principles of faith Mitzvot (613) Halakha Shabbat Holidays Prayer Tzedakah Land of Israel Brit Bar and bat mitzvah Marriage Bereavement Baal teshuva Philosophy Ethics Kabbalah Customs Rites Synagogue Rabbi Texts Ta...

Swan River Rowing Club

Rowing club in Perth, Western Australia The club's Barrack Street shed in about 1910, with Perth City Baths in the background. The Swan River Rowing Club is a rowing club that was founded in 1887 in Perth, Western Australia. It has had rowing sheds at different locations on the Swan River.[1] The Canning River was a location of regattas and social events for the club.[2] In early years regattas were held to increase interest and membership.[3] Social activities were an...

Cadena COPE

Spain's national radio station This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Cadena COPE – news · newspapers · books · scholar · JSTOR (April 2024) (Learn how and when to remove this message) Cadena COPEBroadcast areaSpainBrandingCadena COPEProgrammingLanguage(s)SpanishFormatFull-service and religiousOwnershipOwnerRadio Pop...

Navas del Madroño

Navas del Madroñocomune Navas del Madroño – Veduta LocalizzazioneStato Spagna Comunità autonoma Estremadura Provincia Cáceres TerritorioCoordinate39°37′23.88″N 6°39′03.96″W39°37′23.88″N, 6°39′03.96″W (Navas del Madroño) Altitudine428 m s.l.m. Superficie112,29 km² Abitanti1 555 (2001) Densità13,85 ab./km² Comuni confinantiAlcántara, Arroyo de la Luz, Brozas, Casar de Cáceres, Garrovillas de Alconétar Altre informazioniCod. pos...

Treffendel

TreffendelcomuneTreffendel – Veduta LocalizzazioneStato Francia Regione Bretagna Dipartimento Ille-et-Vilaine ArrondissementRennes CantoneMontfort-sur-Meu TerritorioCoordinate48°02′N 2°00′W48°02′N, 2°00′W (Treffendel) Altitudine130, 56 e 143 m s.l.m. Superficie18,88 km² Abitanti1 270[1] (2009) Densità67,27 ab./km² Altre informazioniCod. postale35380 Fuso orarioUTC+1 Codice INSEE35340 CartografiaTreffendel Sito istituzionaleModifica d...

Castor and Pollux

Greek mythical twins For other uses, see Castor and Pollux (disambiguation). Heavenly Twins redirects here. For other uses, see Heavenly Twins (disambiguation). Castor and Pollux καστωρ πολυδευκηςTwin gods, patrons of sailors, associated with horsemanshipStatues of Castor and Pollux (3rd century AD)Other names Dioskouroi (Latin, Dioscuri) Gemini Castores Tyndarids Polydeuces (Latin, Pollux) The Two Gods Major cult centerAnakeionMountHorsesGenderMaleFestivalsFeast of the Diosko...

1971 au Canada

Cet article est une ébauche concernant une chronologie ou une date et le Canada. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Éphémérides Chronologie du Canada 1968 1969 1970 1971 1972 1973 1974Décennies au Canada :1940 1950 1960 1970 1980 1990 2000 Chronologie dans le monde 1968 1969 1970 1971 1972 1973 1974Décennies :1940 1950 1960 1970 1980 19...

Nikopol, Bulgaria

Town in northern Bulgaria For other uses, see Nikopol (disambiguation). City in Pleven, BulgariaNikopol НикополCityView of Nikopol from the fortress Coat of armsNikopolLocation of Nikopol within BulgariaCoordinates: 43°42′N 24°54′E / 43.700°N 24.900°E / 43.700; 24.900CountryBulgariaProvincePlevenMunicipalityNikopolGovernment • MayorIvelin Savov (BSP)Area • Total35.185 km2 (13.585 sq mi)Elevation179 m (587 ...