Page 379 - Determinants and Their Applications in Mathematical Physics

364 Bibliography

Y. Ohta, R. Hirota, S. Tsujimoto, T. Imai, Casorati and discrete Gram type
determinant representation of solutions to the discrete KP hierarchy. J. Phys.
Soc. Japan 62 (1993), 1872–1886. [PA (1994), 10461.]
Y. Ohta, K. Kajiwara, J. Matsukidaira, J. Satsuma, Casorati determinant so-
lution for the relativistic Toda lattice equation. J. Math. Phys. 34 (1993),
5190–5204. [PA (1994), 10461; MR 95a: 35137].
K. Okamoto, B¨acklund transformations of classical orthogonal polynomials. Al-
gebraic Analysis Vol. II, Academic Press, Boston, 1988, pp. 647–657. [MR 90j:
33012.]
R. Oldenburger, Higher dimensional determinants. Am. Math. Monthly 47 (1940),
25–33. [MR 1 (1940), 194.]
F.R. Olsen, Some determinants involving Bernoulli and Euler numbers of higher
order. Pacific J. Math. 5 (1955), 259–268. [MR 16 (1955), 988.]
F.R. Olsen, Some special determinants. Am. Math. Monthly 63 (1956), 612.
P.J. Olver, Hyperjacobians, determinantal ideals and weak solutions to vari-
ational problems. Proc. Roy. Soc. Edin. 95 (1983), 317–340. [MR 85c:
58040.]
O. Ore, Some studies of cyclic determinants. Duke Math. J. 18 (1951), 343–354.
[MR 13 (1952), 98.]
A. Ostrowski, Collected Mathematical Papers, Vol. 1, Birkh¨auser, Boston, 1983–
1984. [MR 86m: 01075.]
D. Pandres, On higher ordered differentiation Am. Math. Monthly 64 (1957),
566–572.
D. Pandres, A determinant representation of the classical orthogonal polynomials.
Am. Math. Monthly 67 (1960), 658–659. [MR 24a (1962), 3316.]
D.H. Pandya, A property in determinants. Math. Educ. Sec. B9, no.3, (1975),
56–57. [Zbl 341 (1977), 15008.]
S. Parameswaran, Skew-symmetric determinants. Am. Math. Monthly 61 (1954),
116.
M. Parodi, Sur les polynˆomes de Bessel. C.R. Acad. Sci. Paris S´er. A–B 274
(1972), A1153–1155. [MR 46 (1973), 416.]
E. Pascal, Die Determinanten, Druck und Verlag von B.G. Teubner, Leipzig,
1900.
D. Pelinovsky, Rational solutions of the Kadomtsev–Petviashvili hierarchy and
the dynamics of their poles, 1. New form of a general rational solution. J.
Math. Phys. 35 (1994), 5820–5830. [MR 95h: 58071.]
D. Piccini, Dieudonn´ determinant and invariant real polynomials on gl(n, H).
e
Rendiconte 2 (1982), 31–45. [MR 83k: 55012.]
L.A. Pipes, Cyclical functions and permutation matrices. J. Franklin Inst. 287
(1969), 285–296. [MR 39 (1970), 7148.]
A.V. Pogorelov, A priori estimates for solutions of the equation det(z ij)=
φ(z 1,z 2,...,z n, z, x 1,x 2,...,x n). Dokl. Akad. Nauk SSSR 272 (1983),
792–794. [MR 85i: 35022.]
G. P´olya, G. Szeg¨o, Problems and Theorems in Analysis, Vol.2, Springer-Verlag,
New York, Heidelberg, 1976. [MR 49 (1975), 8781; MR 53 (1977), 2.]