The theory of determinants in the historical order of development, by Sir Thomas Muir.

IRECURRENTS (PERGOLA, 1863) 12 1 7
where, in forming the terms, to be summed, each E may be 0 or any
positive integer subject to the condition
161+62 +3'F + ~,flen
D'OVJDIO, E. (1863).
[Due teoremi di determinauti. Giornale di Mat., i. pp. 135-1039.j
D'Ovidio's first determinant is best viewed as being constructed
by prefixing the row
-~~, 1, 0,0
and the column
P' l:"(p +l)' 2!,(p+2). ' ) '
to the persymmetric recurrent
(!( p)iP(nlp+1) ( 1 21,11, )0
('at-p')2(-p +2)!' '2'1'1,0
Calling it D,,1,,, and performing the operation
cob,-i) Coll,
D'Ovidio at once obtains
Dn)+ Dflp
and thence finally
D n =i,T
P +I)
As a corollary he has of course D, 7i where D~ is a persym~
metric recurrent -exactly like that to which the row and columnwere prefixed; for example,
211,
2!1
4 2! 1!I