cesàro in A Sentence

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    Cesàro's teacher, Eugène Charles Catalan, also disparaged divergent series.

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    Cesàro summation is named for the Italian analyst

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    The(H, 1) sum is Cesàro summation,

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    so G is not Cesàro summable.

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    On the other hand, its Cesàro sum is 1/2.

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    Cesàro summation is named for the Italian analyst Ernesto Cesàro 1859-1906.

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    In 1887, Cesàro came close to stating the definition of(C,

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    In 1891, Ernesto Cesàro expressed hope that divergent series would

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    9

    Whenever a series is Cesàro summable, it is also Abel summable

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    10

    The other commonly formulated generalization of Cesàro summation is the sequence of(C, n) methods.

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    11

    Ernesto Cesàro(12 March 1859- 12 September 1906) was an Italian mathematician who worked in the field of differential geometry.

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    12

    In 1887, Cesàro came close to stating the definition of(C, n) summation, but he gave only a few examples.

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    There are two well-known generalizations of Cesàro summation: the conceptually simpler of these is the sequence of(H, n) methods for natural numbers n.

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    The series 1- 1 + 1- 1 +… is Cesàro-summable in the weakest sense, called(C, 1)-summable, while 1- 2 + 3- 4 +… requires a stronger form of Cesàro's theorem, being(C, 2)-summable.

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    15

    Under Catalan's influence, Cesàro initially referred to the"conventional formulas" for 1- 2n + 3n- 4n +… as"absurd equalities", and in 1883 Cesàro expressed a typical view of the time that the formulas were false but still somehow formally useful.

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    16

    The sequence( tn) of means of partial sums of G is( 1 1, 4 2, 10 3, 20 4,).{\ displaystyle\ left({\ frac{ 1}{ 1}},{\ frac{ 4}{ 2}},{\ frac{ 10}{ 3}},{\ frac{ 20}{ 4}},\ ldots\ right).} This sequence diverges to infinity as well, so G is not Cesàro summable.

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