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For a positive real number 1 < β ≤ 2, whether there exits an identity for ∥ ( ∑ k = n ⌊ β n ⌋ 1 u k ) − 1 ∥. is an interesting open problem.
For a general odd number q ≥ 3, whether there exits a computational formula for ∑ h = 1 q ( h, q ) = 1 R q ( 2 h + 1 ) ⋅ S 1 ( 2 h, q ). is an open problem.
For general odd number q ≥ 3, whether there exits a computational formula for the hybrid mean value ∑ ′ m = 1 q ∑ ′ n = 1 q | K ( m, q ) | 2 ⋅ | K ( n, q ) | 2 ⋅ S 1 ( 2 m ⋅ n ¯, q ). is an open problem.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com