Matches in DBpedia 2014 for { ?s ?p In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.Let {a1, a2,...} be a sequence of real numbers that is either nonincreasing or nondecreasing, and let {b1, b2,...} be a sequence of real or complex numbers. If {an} is nondecreasing, it holds thatand if {an} is nonincreasing, it holds thatwhereIn particular, if the sequence {an} is nonincreasing and nonnegative, it follows thatAbel's inequality follows easily from Abel's transformation, which is the discrete version of integration by parts: If{a1, a2,...} and {b1, b2,...} are sequences of real or complex numbers, it holds that. }
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- Abel's_inequality abstract "In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case.Let {a1, a2,...} be a sequence of real numbers that is either nonincreasing or nondecreasing, and let {b1, b2,...} be a sequence of real or complex numbers. If {an} is nondecreasing, it holds thatand if {an} is nonincreasing, it holds thatwhereIn particular, if the sequence {an} is nonincreasing and nonnegative, it follows thatAbel's inequality follows easily from Abel's transformation, which is the discrete version of integration by parts: If{a1, a2,...} and {b1, b2,...} are sequences of real or complex numbers, it holds that".