Hypergeometric functions

Arnold F. Nikiforov and Vasilii B. Uvarov
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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 IV in Special Functions of Mathematical Physics, 1988, pp 253-294 from Springer

Abstract: Abstract In Chapters II and III we discussed properties of the classical orthogonal polynomials and of Bessel functions. Those functions satisfy differential equations which are special cases of the generalized equation of hypergeometric type 1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyDayaaga % Gaey4kaSYaaSaaaeaacuaHepaDgaacaiaacIcacaWG6bGaaiykaaqa % aiabeo8aZjaacIcacaWG6bGaaiykaaaaceWG1bGbauaacqGHRaWkda % Wcaaqaaiqbeo8aZzaaiaGaaiikaiaadQhacaGGPaaabaGaeq4Wdm3a % aWbaaSqabeaacaaIYaaaaOGaaiikaiaadQhacaGGPaaaaiaadwhacq % GH9aqpcaaIWaaaaa!4E1E! $$u'' + \frac{{\tilde \tau (z)}}{{\sigma (z)}}u' + \frac{{\tilde \sigma (z)}}{{{\sigma ^2}(z)}}u = 0$$ Here σ(z) and σ(z) and % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbaG % aacaGGOaGaamOEaiaacMcaaaa!3A1E! $$\tilde \sigma (z)$$ are polynomials of degree at most 2, and % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqiXdqNbaG % aacaGGOaGaamOEaiaacMcaaaa!3A20! $$\tilde \tau (z)$$ is a polynomial of degree at most 1.

Date: 1988
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DOI: 10.1007/978-1-4757-1595-8_4

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