Series with Hermite polynomials and applications
PUBLICATIONES MATHEMATICAE-DEBRECEN, cilt.80, sa.3-4, ss.385-404, 2012 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 80 Sayı: 3-4
- Basım Tarihi: 2012
- Doi Numarası: 10.5486/pmd.2012.5072
- Dergi Adı: PUBLICATIONES MATHEMATICAE-DEBRECEN
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.385-404
- Anahtar Kelimeler: Hermite polynomials, Laguerre polynomials, harmonic numbers, Fibonacci numbers, exponential numbers, geometric numbers, Stirling numbers of the second kind, binomial transformation, Euler series transformation, generating functions
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Akdeniz Üniversitesi Adresli: Evet
Özet
We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic numbers, Lucas sequences, exponential and geometric numbers. We also obtain a series involving both Hermite and Laguerre polynomials, and a series with Hermite polynomials and Stirling numbers of the second kind.