…
►The introduction to the eigenvalues and the functions of general
order proceeds as in §§
28.2(i),
28.2(ii), and
28.2(iii), except that we now restrict
; equivalently
.
…
►
§28.12(ii) Eigenfunctions
…
►For
,
…
►
…
►
…
►The results have been published in book form as the
NIST Handbook of Mathematical Functions, by
Cambridge University Press, and disseminated in the
free electronic
Digital Library of Mathematical Functions.
…
►They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information
online and in handbooks; and in the presentation of mathematics on the web.
…
…
►The general second-
order Fuchsian equation with
regular singularities at
,
, and at
, is given by
…The three sets of parameters comprise the
singularity parameters
, the
exponent parameters
, and the
free accessory parameters
.
With
and
the total number of
free parameters is
.
…
►An algorithm given in
Kovacic (1986) determines if a given (not necessarily Fuchsian) second-
order homogeneous linear differential equation with rational coefficients has solutions expressible in finite terms (Liouvillean solutions).
…
…
►In this regard, he has been exploring mathematical knowledge management and the digital expression of mostly unambiguous context-
free full semantic information for mathematical formulae.
…
►The new
DLMF (Digital Library of Mathematical Functions) will appear in a hardcover edition and as a
free electronic publication on the World
Wide Web.
…
…
►These parameters, including
, are not
free: they are determined by a compact, connected Riemann surface (
Krichever (1976)), or alternatively by an appropriate initial condition
(
Deconinck and Segur (1998)).
…
►Furthermore, the solutions of the KP equation solve the
Schottky
problem: this is the question concerning conditions that a Riemann matrix needs to satisfy in
order to be associated with a Riemann surface (
Schottky (1903)).
…