L’Hôpital rule for derivatives
(0.003 seconds)
11—20 of 348 matching pages
11: 23.6 Relations to Other Functions
…
►In this subsection , are any pair of generators of the lattice , and the lattice roots , , are given by (23.3.9).
…
►
23.6.13
►
23.6.14
…
►Again, in Equations (23.6.16)–(23.6.26), are any pair of generators of the lattice and are given by (23.3.9).
…
►Also, , , are the lattices with generators , , , respectively.
…
12: 18.39 Applications in the Physical Sciences
…
►where is the (squared) angular momentum operator (14.30.12).
…
►with an infinite set of orthonormal eigenfunctions
… here being the order of the Laguerre polynomial, of Table 18.8.1, line 11, and the angular momentum quantum number, and where
…
►The bound state eigenfunctions of the radial Coulomb Schrödinger operator are discussed in §§18.39(i) and 18.39(ii), and the -function normalized (non-) in Chapter 33, where the solutions appear as Whittaker functions.
…
►The fact that non- continuum scattering eigenstates may be expressed in terms or (infinite) sums of functions allows a reformulation of scattering theory in atomic physics wherein no non- functions need appear.
…
13: 29.1 Special Notation
…
►All derivatives are denoted by differentials, not by primes.
…
►The relation to the Lamé functions , of Jansen (1977) is given by
►
►
►
…
14: 18.5 Explicit Representations
…
►
…
►
►
…
18.5.6
…
►Similarly in the cases of the ultraspherical polynomials and the Laguerre polynomials we assume that , and , unless
stated otherwise.
…
►
15: 18.17 Integrals
…
►
18.17.2
…
►Formulas (18.17.9), (18.17.10) and (18.17.11) are fractional generalizations of -th derivative formulas which are, after substitution of (18.5.7), special cases of (15.5.4), (15.5.5) and (15.5.3), respectively.
…
►
18.17.15
.
►Formulas (18.17.14) and (18.17.15) are fractional generalizations of -th derivative formulas which are, after substitution of (13.6.19), special cases of (13.3.18) and (13.3.20), respectively.
…
►
18.17.47
…
16: 11.2 Definitions
…
►The functions and are entire functions of and .
…
►
11.2.4
…
►Unless indicated otherwise, , , , and assume their principal values throughout the DLMF.
…
►
11.2.10
…
►
11.2.16
…
17: 18.4 Graphics
18: 3.2 Linear Algebra
…
►With the process of solution can then be regarded as first solving the equation for (forward
elimination), followed by the solution of for (back substitution).
…
►Because of rounding errors, the residual vector
is nonzero as a rule.
…
►
…
3.2.8
…
►In the case that the orthogonality condition is replaced by -orthogonality, that is, , , for some positive definite matrix with Cholesky decomposition , then the details change as follows.
…
►
19: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
…
►