Index L
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L’Hôpital’s rule for derivatives
§1.4(iii)
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Lagrange interpolation
§3.3(i)—§3.3(ii)
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Lagrange inversion theorem
§1.10(vii)
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Lagrange’s formula for reversion of series
§2.2
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Laguerre functions
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Laguerre polynomials §18.3, see also classical orthogonal polynomials.
-
addition theorem
§18.18(ii)
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applications
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asymptotic approximations
§18.15(iv)—§18.15(iv)
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computation
Ch.18
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continued fraction
§18.13
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derivatives
§18.9(iii)
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differential equations
Table 18.8.1
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Dirac delta
§1.17(iii)
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expansions in series of §18.18(iii), §18.18(i), §18.18(ii)
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explicit representations
§18.5—§18.5(iv)
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Fourier transforms
§18.17(v)
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generalized
§18.1(ii)
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generating functions
§18.12
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graphics Figure 18.4.5, Figure 18.4.5, Figure 18.4.5, Figure 18.4.6, Figure 18.4.6, Figure 18.4.6
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inequalities §18.14(iii), §18.14(i), §18.14(ii)
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integral representations §18.10(ii), §18.10(iv), Table 18.10.1
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integrals §18.17(iv), §18.17(vi), §18.17(i)
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interrelations with other orthogonal polynomials Figure 18.21.1, Figure 18.21.1, Figure 18.21.1, §18.21(ii), §18.21(ii), §18.7(iii), §18.7(iii)
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Laplace transform
§18.17(vi)
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leading coefficients
Table 18.3.1
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limiting form as a Bessel function
§18.11(ii)
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limits to monomials
§18.6(ii)
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local maxima and minima
§18.14(iii)
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Mellin transform
§18.17(vii)
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monic
§3.5(v)
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multiplication theorem
§18.18(iii)
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normalization
Table 18.3.1
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notation
§18.1(ii)
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orthogonality properties
Table 18.3.1
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parameter constraint Table 18.3.1, §18.5(iii)
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Poisson kernels
§18.18(vii)
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recurrence relations
Table 18.9.1
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relation to confluent hypergeometric functions §13.18(v), §13.6(v), §18.11(i), §18.5(iii)
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Rodrigues formula
Table 18.5.1
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tables
§18.41(i)
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tables of zeros Table 3.5.7, Table 3.5.8, Table 3.5.9
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upper bounds
§18.14(i)
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value at
§18.6(i)
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weight function
Table 18.3.1
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zeros §18.16(iv), §18.2(vi)
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Lambert series
-
Lambert -function
§4.13
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Lamé functions
Ch.29
-
Lamé polynomials
Ch.29
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Lamé wave equation
§29.11
-
Lamé–Wangerin functions
§29.17(iii)
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Lamé’s equation
§29.2(i)
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Lanczos tridiagonalization of a symmetric matrix
§3.2(vi)
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Lanczos vectors
§3.2(vi)
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Landen transformations
-
Laplace equation
-
Laplace transform
-
Laplace’s equation
-
Laplace’s method for asymptotic expansions of integrals §2.3(iii), §2.4(iii)
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Laplacian
§1.5(ii)
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lattice
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lattice models of critical phenomena
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lattice parameter
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lattice paths
§26.2—§26.6(iv)
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lattice walks
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Laurent series
§1.10(iii)
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asymptotic approximations for coefficients
§2.10(iv)
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Lauricella’s function
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Lax pairs