The Classical Orthogonal Polynomials

Arnold F. Nikiforov and Vasilii B. Uvarov
Additional contact information
Arnold F. Nikiforov: M.V. Keldish Institute of Applied Mathematics of the Academy of Sciences of the USSR
Vasilii B. Uvarov: M.V. Keldish Institute of Applied Mathematics of the Academy of Sciences of the USSR

Chapter Chapter II in Special Functions of Mathematical Physics, 1988, pp 21-200 from Springer

Abstract: Abstract In §2 we introduced the polynomials y n (z) of hypergeometric type, which are solutions of (1) % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aae % WaaeaacaWG6baacaGLOaGaayzkaaGabmyEayaagaGaey4kaSIaeqiX % dq3aaeWaaeaacaWG6baacaGLOaGaayzkaaGabmyEayaafaGaey4kaS % Iaeq4UdWMaamyEaiabg2da9iaaicdaaaa!46D7! $$\sigma \left( z \right)y'' + \tau \left( z \right)y' + \lambda y = 0$$ with % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdWMaey % ypa0Jaeq4UdW2aaSbaaSqaaiaad6gaaeqaaOGaeyypa0JaeyOeI0Ia % amOBaiqbes8a0zaafaGaeyOeI0YaaSaaaeaacaaIXaaabaGaaGOmaa % aacaWGUbWaaeWaaeaacaWGUbGaeyOeI0IaaGymaaGaayjkaiaawMca % aiqbeo8aZzaagaaaaa!499D! $$\lambda = {\lambda _n} = - n\tau ' - \frac{1}{2}n\left( {n - 1} \right)\sigma ''$$

Keywords: Orthogonal Polynomial; Spherical Harmonic; Hermite Polynomial; Jacobi Polynomial; Polynomial Solution (search for similar items in EconPapers)
Date: 1988
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-1595-8_2

Ordering information: This item can be ordered from
http://www.springer.com/9781475715958

DOI: 10.1007/978-1-4757-1595-8_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().