recurrence relation

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21: 26.3 Lattice Paths: Binomial Coefficients

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§26.3(iii) Recurrence Relations

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22: 18.33 Polynomials Orthogonal on the Unit Circle

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§18.33(ii) Recurrence Relations

… ►For an alternative and more detailed approach to the recurrence relations, see §18.33(vi). … ►

Recurrence Relations

… ►Equivalent to the recurrence relations (18.33.23), (18.33.24) are the inverse Szegő recurrence relations … ►while combination of (18.33.27) and (18.33.23) gives the three-term recurrence relation …

23: 14.21 Definitions and Basic Properties

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§14.21(iii) Properties

… ►This includes, for example, the Wronskian relations (14.2.7)–(14.2.11); hypergeometric representations (14.3.6)–(14.3.10) and (14.3.15)–(14.3.20); results for integer orders (14.6.3)–(14.6.5), (14.6.7), (14.6.8), (14.7.6), (14.7.7), and (14.7.11)–(14.7.16); behavior at singularities (14.8.7)–(14.8.16); connection formulas (14.9.11)–(14.9.16); recurrence relations (14.10.3)–(14.10.7). …

24: 15.19 Methods of Computation

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§15.19(iv) Recurrence Relations

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25: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions

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§26.4(iii) Recurrence Relation

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26: 26.9 Integer Partitions: Restricted Number and Part Size

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§26.9(iii) Recurrence Relations

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27: 26.6 Other Lattice Path Numbers

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§26.6(iii) Recurrence Relations

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26.6.10 $$D(m,n)=D(m,n-1)+D(m-1,n)+D(m-1,n-1),$$ $m,n\ge 1$,

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Symbols:

$m$: nonnegative integer, $n$: nonnegative integer and $D(m,n)$: Delannoy number

Referenced by:

§26.6(iii)

Permalink:

http://dlmf.nist.gov/26.6.E10

Encodings:

pMML, png, TeX

See also:

Annotations for §26.6(iii), §26.6 and Ch.26

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28: 28.14 Fourier Series

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28.14.4 $$q{c}_{2m+2}-\left(a-{(\nu +2m)}^2\right)c_{2m}+q{c}_{2m-2}=0,$$ $a={\lambda }_{\nu }\left(q\right),c_{2m}=c_{2m}^{\nu }(q)$,

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Symbols:

${\lambda }_{\nu +2n}\left(q\right)$: eigenvalues of Mathieu equation, $m$: integer, $q=h^2$: parameter, $\nu$: complex parameter, $a$: parameter and $c_{2m}(q)$: coefficients

Referenced by:

item (d), item (d)

Permalink:

http://dlmf.nist.gov/28.14.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §28.14 and Ch.28

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29: 13.29 Methods of Computation

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§13.29(iv) Recurrence Relations

►The recurrence relations in §§13.3(i) and 13.15(i) can be used to compute the confluent hypergeometric functions in an efficient way. …

30: 10.74 Methods of Computation

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§10.74(iv) Recurrence Relations

►If values of the Bessel functions $J_{\nu }\left(z\right)$, $Y_{\nu }\left(z\right)$, or the other functions treated in this chapter, are needed for integer-spaced ranges of values of the order $\nu$, then a simple and powerful procedure is provided by recurrence relations typified by the first of (10.6.1). …