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Formula:215

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Digital Library of Mathematical Functions ID 1.7.E3

( βˆ‘ j = 1 n ( a j + b j ) p ) 1 / p ≀ ( βˆ‘ j = 1 n a j p ) 1 / p + ( βˆ‘ j = 1 n b j p ) 1 / p . superscript subscript superscript 𝑛 𝑗 1 superscript subscript π‘Ž 𝑗 subscript 𝑏 𝑗 𝑝 1 𝑝 superscript subscript superscript 𝑛 𝑗 1 superscript subscript π‘Ž 𝑗 𝑝 1 𝑝 superscript subscript superscript 𝑛 𝑗 1 superscript subscript 𝑏 𝑗 𝑝 1 𝑝 {\displaystyle{\displaystyle\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p}% \leq\left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}% \right)^{1/p}.}}


Constraint(s)

Symbols List

  • j 𝑗 {\displaystyle{\displaystyle j}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • p > 1 𝑝 1 {\displaystyle{\displaystyle p>1}} : > p 1
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This page was last edited on 28 January 2024, at 10:30.
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