Szegő recurrence relations

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11: 26.5 Lattice Paths: Catalan Numbers

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§26.5(i) Definitions

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§26.5(iii) Recurrence Relations

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12: 5.5 Functional Relations

§5.5 Functional Relations

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§5.5(i) Recurrence

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5.5.1 $$\mathrm{\Gamma }\left(z+1\right)=z\mathrm{\Gamma }\left(z\right),$$

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Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function and $z$: complex variable

A&S Ref:

6.1.15

Referenced by:

§15.4(ii), §15.4(iii), (25.11.27), (25.5.6), §5.4(i)

Permalink:

http://dlmf.nist.gov/5.5.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §5.5(i), §5.5 and Ch.5

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13: 12.8 Recurrence Relations and Derivatives

§12.8 Recurrence Relations and Derivatives

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§12.8(i) Recurrence Relations

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14: 14.10 Recurrence Relations and Derivatives

§14.10 Recurrence Relations and Derivatives

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15: 32.15 Orthogonal Polynomials

… ►with recurrence relation …Then $u_n(z)={(a_n(z))}^2$ satisfies the nonlinear recurrence relation …

16: 13.27 Mathematical Applications

… ►This identification can be used to obtain various properties of the Whittaker functions, including recurrence relations and derivatives. …

17: 14.32 Methods of Computation

… ►In other cases recurrence relations (§14.10) provide a powerful method when applied in a stable direction (§3.6); see Olver and Smith (1983) and Gautschi (1967). …

18: 10.6 Recurrence Relations and Derivatives

§10.6 Recurrence Relations and Derivatives

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§10.6(i) Recurrence Relations

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§10.6(iii) Cross-Products

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19: 26.3 Lattice Paths: Binomial Coefficients

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§26.3(i) Definitions

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§26.3(iii) Recurrence Relations

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20: 3.10 Continued Fractions

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Forward Recurrence Algorithm

►The $A_n$ and $B_n$ of (3.10.2) can be computed by means of three-term recurrence relations (1.12.5). … ►

Backward Recurrence Algorithm

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Forward Series Recurrence Algorithm

… ►This forward algorithm achieves efficiency and stability in the computation of the convergents $C_n=A_n/B_n$, and is related to the forward series recurrence algorithm. …