DE FUNCTIONIBUS TRANSSCENDENTIBUS QUAE EX DIFFERENTIATIONE ETC.
373
l
d® i dy f
x ~F y * * ’
dar dy
x y 9
unde statini prodit
/= ì^+'Ì+^+t ) =/+*£(*-*)+*£(*-*)
1?JL
dar'
ar'
\<hl
y'
=/.
dar"
ar"
dar'
_dl
r
: n
dar"
ar'
y'
tf i
ar"
=/+•** V
etc.
et prorsus simili modo
/"=/+ +a' ^ • /'"=/"+ i/ ^
Perinde fit
9 = = +£(•-*)++£(*—0 =
eodemque modo g" = g" = \g" x ^*~ etc. Nec non hinc patet esse
/== /+/, /" = /+/+/. /"' = /4-/+/+/" etc. Nullo negotio perspici
tur , seriem —, —, — etc. celerrime infra omnes limites decrescere, quamobrem
habebimus per seriem infinitam rapidissime convergentem
hinc
/“=/+all^
2 dar* 2d?/ 00
x — ar a; — a;
a;' 1 a:
2 d M (ar, ?/)
y 00 M (ar, ?/)
dar , d?/ dar d?/1
. x — ar' ar'—ar" ar"—x'" . . 1 00 A
■ + +etc. , £ =0
dar , a?/ r ax
x ' y "* < x
dM(<r,j/) = M [pc,y) X Ì^X(i+
( . X X , . X X X X li)
x i hi——•—— + etc. sive
y 1 i X y > ' 1 X 1 4 a; x 1
x — x x — ar‘
+ ^x(w
X X X X
Calculum aliquantum commodiorem nanciscimur sequenti modo: Fit
x — x' x- y (x — yf {x -p yf — 4 ary ^ x'x' y'y ^
ar' x-\-y xx — yy * xx — yy xx — yy
unde promanat
dM(<a?, y)=X | ~X[xx —yy+2[ococ—yy )-f-4{pc"x"—y”y")-f-8[x"'x"—y'"y"')■ ■)
dy.
-h — X[XX —yy— 2[OC00—yy') — 4[oé'oc'—yy ) — 8{oc"oc"—y"y")...)(
y
.. . , ar—ar ar ar —y y x —ar ar ar —y y
*) et perinde — = 4 ———, —- = 4 - „ „ „ — etc -
ar xx — y y x xx — y y