Formeln und Sätze für die Speziellen Funktionen der Mathematischen Physik

Magnus, Wilhelm; Oberhettinger, Fritz

doi:10.1007/978-3-662-41791-1

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Polynomials Orthogonal On the Unit Circle1

Fundamental and Singular Solutions Of Lamé Equations 4651

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2007

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Cited by 115 publications

(50 citation statements)

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“…Namely, one has [17] K(e ±iφ ) = 1 2 e ∓iφ/2 (K(cos(φ/2)) ± iK(sin(φ/2))), −π < φ ≤ π, whence we have…”

Section: Polynomials Orthogonal On the Unit Circlementioning

confidence: 99%

Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Vinet

Zhedanov²

2007

SIGMA

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Abstract. We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, explicit expression and the weight function for these polynomials are obtained. We construct also a new explicit example of the Szegö polynomials orthogonal on the unit circle. Relations with associated Legendre polynomials are considered. Vadim Kuznetsov spent a number of years at the Centre de Recherches Mathématiques of the Université de Montréal in the mid-90s. This is when we had the privilege to have him as a colleague and the chance to appreciate his scientif ic and human qualities. His smile, great spirit, penetrating insights and outstanding scientif ic contributions will always be with us.

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“…Namely, one has [17] K(e ±iφ ) = 1 2 e ∓iφ/2 (K(cos(φ/2)) ± iK(sin(φ/2))), −π < φ ≤ π, whence we have…”

Section: Polynomials Orthogonal On the Unit Circlementioning

confidence: 99%

Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction

Vinet

Zhedanov²

2007

SIGMA

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“…The associated Legendre functions P k n can also be obtained by combination of two recurrence relations, which are mainly due to Magnus and Oberhettinger [36]:…”

Section: Fundamental and Singular Solutions Of Lamé Equations 465mentioning

confidence: 99%

Fundamental and singular solutions of Lamé equations for media with arbitrary elastic anisotropy

Kuznetsov

2005

Quart. Appl. Math.

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“…Since the present writer knows of no place where to find explicit expressions for some more of Legendres associated functions of the second kind than are given for instance in [1] or [2], he hopes the small collection of formulae at the end of this note might be of some use to others.…”

mentioning

confidence: 99%

“…The associated Legendre functions Qnk(x) of the second kind f or | x | > land nonnegative integer values of n, k can be defined by [1] i dk 2dx…”

mentioning

confidence: 99%