Rit (Vísindafélag Íslendinga) - 01.06.1951, Blaðsíða 3

1. INTRODUCTION
My chief purpose is to shovv how easily the serial rela-
tious, previously described by me, in connexion with Sym-
bolic Calculus lead to mathematical formulae. Most of these
fornnilae are wellknown but some have not hitherto receiv
ed adequate attention according to my view.
The infinite series dealt with in present paper are those
') 0|. (P“)
I previously have signified with y
I define these infinite series as follows: --
where
U=y~ «n X” (1)
n o
"to"= ddxn , « - 0,1, 2, 3. (2)
’ = - . - o„ being a definite func-
dxn (ixn ; ,v 0;
tion of ii, usually a known function. Sometimes we call y
the generatrix funcion of ^ (n)=n!a„. The determination of
U from (2) may be carried out by the conversion formula:i)
or by other methods. I shall not at present enter on further
mention of tliese methods, as they will be discussed exten-
sively on the following pages. Now 1 shall only point out
that the determination of y by ihese methods is quite
independent of convergence or divergence of the series
«„ xn. I have elsewhere4) shown tliat we can deal with