Minkowski inequalities for sums and series
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11—20 of 200 matching pages
11: 1.9 Calculus of a Complex Variable
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►Then the series
converges uniformly on .
►A doubly-infinite series
converges (uniformly) on iff each of the series
and converges (uniformly) on .
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►Inside the circle the sum of the series is an analytic function .
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►A double series is the limit of the double sequence
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►If a double series is absolutely convergent, then it is also convergent and its sum is given by either of the repeated sums
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12: 28.19 Expansions in Series of Functions
§28.19 Expansions in Series of Functions
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28.19.2
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►The series (28.19.2) converges absolutely and uniformly on compact subsets within .
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28.19.4
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13: 5.7 Series Expansions
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►
5.7.3
.
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14: 8.7 Series Expansions
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►
8.7.6
, .
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15: 28.30 Expansions in Series of Eigenfunctions
§28.30 Expansions in Series of Eigenfunctions
… ►Then every continuous -periodic function whose second derivative is square-integrable over the interval can be expanded in a uniformly and absolutely convergent series ►
28.30.3
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16: 27.5 Inversion Formulas
17: Bibliography
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Monotonicity theorems and inequalities for the complete elliptic integrals.
J. Comput. Appl. Math. 172 (2), pp. 289–312.
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A harmonic mean inequality for the gamma function.
J. Comput. Appl. Math. 87 (2), pp. 195–198.
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On some inequalities for the incomplete gamma function.
Math. Comp. 66 (218), pp. 771–778.
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Gamma function inequalities.
Numer. Algorithms 49 (1-4), pp. 53–84.
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Inequalities for elliptic integrals.
Publ. Inst. Math. (Beograd) (N.S.) 37(51), pp. 61–63.
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18: 9.19 Approximations
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►The constants and are chosen numerically, with a view to equalizing the effort required for summing the series.
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19: 25.8 Sums
20: 33.23 Methods of Computation
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►Cancellation errors increase with increases in and , and may be estimated by comparing the final sum of the series with the largest partial sum.
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