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Digital Library of Mathematical Functions ID
1.7.E2
∑
j
=
1
n
a
j
b
j
≤
(
∑
j
=
1
n
a
j
p
)
1
/
p
(
∑
j
=
1
n
b
j
q
)
1
/
q
.
subscript
superscript
𝑛
𝑗
1
subscript
𝑎
𝑗
subscript
𝑏
𝑗
superscript
subscript
superscript
𝑛
𝑗
1
superscript
subscript
𝑎
𝑗
𝑝
1
𝑝
superscript
subscript
superscript
𝑛
𝑗
1
superscript
subscript
𝑏
𝑗
𝑞
1
𝑞
{\displaystyle{\displaystyle\sum^{n}_{j=1}a_{j}b_{j}\leq\left(\sum^{n}_{j=1}a_% {j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}.}}
Constraint(s)
Symbols List
j
𝑗
{\displaystyle{\displaystyle j}}
: integer
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
q
𝑞
{\displaystyle{\displaystyle q}}
: number
p
>
1
𝑝
1
{\displaystyle{\displaystyle p>1}}
: > p 1
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