533]
FACTORIALS, AND DERIVATIONS.
467
where the symbols ( ) 0 denote sums of products of the differences of
and a lower letter, 6 factors in each product; and the several sums
follows :
For
a, ¡3, y, 8, e
a, b, c, d, e)i
write a
/3
7
8
a
b
c
d
e;
the expression is
For
(a — a) 4- (/3 — b) + (y — c) + (8 — d) + (e — e).
a, /3, y, 8
m, b, c, d, e,
a, a
a, 8
a, /3
a, c
a, y
a, o?
/3, /3
c
a, 8
a, e
/3, y
6, d
/3, 8
b, e
7> 7
c, d
7» $
c, e
8, 8
d, e
viz. the expression is
(a — a) (a — b) + (a — a) (/3 — c) + ... + (8 — d) (8 — e).
For
write a,
a , a
a,
b,
c
a,
a, /3
a,
b,
d
a,
a, y
a,
b,
e
a,
/8, /8
a,
c,
d
a,
/3, y
a,
C,
e
/3,
/3, /3
b,
C,
d
a,
7. 7
a,
d,
e
/3,
/3, 7
b,
c,
e
A
7> 7
b,
d,
e
7>
7’ 7
c,
d,
e
viz. the expression is
(a — a) (a - b) (a — c) + ... + (y — c) (y — d) (y — e).
an upper letter
being formed as