with real periods
(0.003 seconds)
1—10 of 55 matching pages
1: 25.13 Periodic Zeta Function
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►The notation is used for the polylogarithm with
real:
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25.13.1
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25.13.2
, ,
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25.13.3
if ; if .
2: 29.3 Definitions and Basic Properties
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►For each pair of values of and there are four infinite unbounded sets of real eigenvalues for which equation (29.2.1) has even or odd solutions with periods
or .
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►They are called Lamé functions with real periods and of order
, or more simply, Lamé functions.
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3: 29.12 Definitions
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4: 25.2 Definition and Expansions
5: 25.11 Hurwitz Zeta Function
6: 24.2 Definitions and Generating Functions
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,
.
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7: 3.5 Quadrature
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►If in addition is periodic, , and the integral is taken over a period, then
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►The integrand can be extended as a periodic
function on with period
and as noted in §3.5(i), the trapezoidal rule is exceptionally efficient in this case.
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8: 24.17 Mathematical Applications
9: 22.2 Definitions
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►As a function of , with fixed , each of the 12 Jacobian elliptic functions is doubly periodic, having two periods whose ratio is not real.
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