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11—20 of 139 matching pages
11: Bibliography T
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Laguerre polynomials: Asymptotics for large degree.
Technical report
Technical Report AM-R8610, CWI, Amsterdam, The Netherlands.
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Algorithm 165: Complete elliptic integrals.
Comm. ACM 6 (4), pp. 163–164.
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12: Ingram Olkin
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►Olkin’s degrees are B.
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►He also was a Guggenheim, Fulbright, Humboldt, and Lady Davis Fellow, had an honorary degree from De Montfort University, and was awarded the Townsend Harris Medal by the City University of New York.
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13: 14.1 Special Notation
§14.1 Special Notation
… ►, , | real variables. |
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… | |
, | unless stated otherwise, nonnegative integers, used for order and degree, respectively. |
, | general order and degree, respectively. |
complex degree, . | |
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14: 31.8 Solutions via Quadratures
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31.8.2
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►Here is a polynomial of degree
in and of degree
in , that is a solution of the third-order differential equation satisfied by a product of any two solutions of Heun’s equation.
The degree
is given by
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31.8.3
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15: 14.31 Other Applications
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§14.31(iii) Miscellaneous
… ►Legendre functions of complex degree appear in the application of complex angular momentum techniques to atomic and molecular scattering (Connor and Mackay (1979)). …16: 3.5 Quadrature
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►with weight function
, is one for which whenever is a polynomial of degree
.
The nodes
are prescribed, and the weights
and error term
are found by integrating the product of the Lagrange interpolation polynomial of degree
and .
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►Let denote the set of monic polynomials of degree
(coefficient of equal to ) that are orthogonal with respect to a positive weight function on a finite or infinite interval ; compare §18.2(i).
…As a consequence, the rule is exact for any polynomial of degree
, that is,
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►where if is a polynomial of degree
in .
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17: 14.11 Derivatives with Respect to Degree or Order
18: 14.14 Continued Fractions
19: 30.5 Functions of the Second Kind
20: George E. Andrews
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►He holds honorary degrees from the Universities of Parma, Florida, Waterloo, Illinois, and SASTRA University (India).
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