Konfluent hipergeometrik fonksiyonlar ve uygulamaları
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Dosyalar
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Hitit Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu çalışmada hipergeometrik fonksiyonların bir alt grubu olan konfluent hipergeometrik fonksiyonlar ve bu fonksiyonların uygulamaları incelenmiştir. Öncelikle hipergeometrik diferansiyel denklemin genel yapısı ortaya konulmuş ve bazı özelliklerinden bahsedilmiştir. Hipergeometrik diferansiyel denklemde kullanılan özel dönüşümler yardımıyla konfluent hipergeometrik diferansiyel denklem oluşturulmuştur. Bu denklemin çözümleri olarak kabul edilen konfluent hipergeometrik fonksiyonların integral ve seri gösterimleri elde edilmiştir. Ayrıca konfluent hipergeometrik diferansiyel denklemin kuantum fizikteki bazı uygulamaları araştırılmıştır. Bununla birlikte taktik füze sistemi modellenmesi sonucu elde edilen denklem sistemlerinin belirli varsayımlar ve dönüşümler yardımıyla konfluent diferansiyel denkleme dönüştürülebileceği gösterilmiş ve çözümleri konfluent hipergeometrik fonksiyonlar cinsinden yazılmıştır.
In this study, confluent hypergeometric functions which are considered as a subgroup of hypergeometric functions, and their applications are investigated. First of all, the general structure of hypergeometric differential equation is presented and its some properties are mentioned. Confluent hypergeometric differential equation was established from hypergeometric differential equation with the help of special transformations. Integral and series representations of confluent hypergeometric functions which are accepted as solutions of confluent hypergeometric differential equation are obtained. In addition, some applications of the confluent hypergeometric differential equation in quantum physics are investigated. Moreover, it has been shown that the equation system obtained from tactical missile system modeling can be converted into confluent differential equation by means of certain assumptions and transformations, and their solutions are expressible in terms of confluent hypergeometric functions.
In this study, confluent hypergeometric functions which are considered as a subgroup of hypergeometric functions, and their applications are investigated. First of all, the general structure of hypergeometric differential equation is presented and its some properties are mentioned. Confluent hypergeometric differential equation was established from hypergeometric differential equation with the help of special transformations. Integral and series representations of confluent hypergeometric functions which are accepted as solutions of confluent hypergeometric differential equation are obtained. In addition, some applications of the confluent hypergeometric differential equation in quantum physics are investigated. Moreover, it has been shown that the equation system obtained from tactical missile system modeling can be converted into confluent differential equation by means of certain assumptions and transformations, and their solutions are expressible in terms of confluent hypergeometric functions.
Açıklama
Anahtar Kelimeler
Hipergeometrik diferansiyel denklem, Konfluent fonksiyonlar, İntegral ve seri gösterimleri, Taktik füze sistemi, Hypergeometric differential equation, Confluent functions, İntegral and series representations, Tactical missile system
Kaynak
WoS Q Değeri
Scopus Q Değeri
Cilt
Sayı
Künye
Akgül, Hasan (2022). Konfluent hipergeometrik fonksiyonlar ve uygulamaları. (Yayınlanmamış Yüksek Lisans Tezi). Hitit Üniversitesi, Lisansüstü Eğitim Enstitüsü, Matematik Anabilim Dalı
