1549901369-Elements_of_Real_Analysis__Denlinger_

724 Glossary of Symbols

Symbol

p

n

S.(f, P) = L mil:,.i

i=l n

S(f, P) = L Mil:,.i

b -b

J - a f , J af

I: f

llPll

P*

i=l

n

THE RIEMANN INTEGRAL

Meaning Defined on page

partition of [a, b]

inf{J(x) : x E [xi-1, xi]}

sup{f(x) : x E [xi-1, xi]}

Xi - Xi-1

lower Darboux sum of f over P

upper Darboux sum of f over P

lower (upper) Darboux integrals off over [a, b]

Riemann integral off over [a, b]

mesh of the partition P

tagged partition of [a, b]

360

361

361

361

361

361

363

364

372

374

R(f, P*) = L f(x;)t::,.i Riemann sum off over tagged partition P * 374

i=l

regular partition of [a, b] into n subintervals

jump of f at xo

379

392

fa+oo f, J~ 00 f, J~;: f (improper) integrals of f over infinite intervals 438, 439

Symbol
00
L ak (= S)
k=l
n
Sn = L ak
k=l
a;t, a;;:
X' = (x1,X2,···Xn)
]Rn
X'. if
00
I: ak(x - c)k
k=l
p

(%)

00

L%

i,j=l

SERIES OF REAL NUMBERS

Meaning Defined on page

an infinite series of numbers with sum S 453

00

nth partial sum of I: ak 453

k=l

max{ an, O}, max{-an, O} 480

an n-vector 498

Euclidean n-space 498

dot product of X' and if 499

a power series in ( x - c) 504

radius of convergence of a power series 506

binomial coefficient for arbitrary a E JR, n E N 523

a double series 529