on critical line or strip
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11: 4.3 Graphics
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►Figure 4.3.2 illustrates the conformal mapping of the strip
onto the whole -plane cut along the negative real axis, where and (principal value).
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12: 28.29 Definitions and Basic Properties
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is either a continuous and real-valued function for or an analytic function of in a doubly-infinite open strip that contains the real axis.
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►For further results, especially when is analytic in a strip, see Weinstein and Keller (1987).
13: Bibliography V
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On the zeros of the Riemann zeta function in the critical strip. IV.
Math. Comp. 46 (174), pp. 667–681.
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14: 4.15 Graphics
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►Figure 4.15.7 illustrates the conformal mapping of the strip
onto the whole -plane cut along the real axis from to and to , where and (principal value).
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15: 2.5 Mellin Transform Methods
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►The domain of analyticity of is usually an infinite strip
parallel to the imaginary axis.
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►If and have a common strip of analyticity , then
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►The sum in (2.5.6) is taken over all poles of in the strip
, and it provides the asymptotic expansion of for small values of .
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►To apply the Mellin transform method outlined in §2.5(i), we require the transforms and to have a common strip of analyticity.
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16: 28.8 Asymptotic Expansions for Large
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►They are uniform with respect to when , where is an arbitrary constant such that , and also with respect to in the semi-infinite strip given by and .
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17: 1.5 Calculus of Two or More Variables
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►Suppose that are finite, is finite or , and , are continuous on the partly-closed rectangle or infinite strip
.
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18: 2.10 Sums and Sequences
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(a)
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On the strip , is analytic in its interior, is continuous on its closure, and as , uniformly with respect to .
19: 28.28 Integrals, Integral Representations, and Integral Equations
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►In particular, when the integrals (28.28.11), (28.28.14) converge absolutely and uniformly in the half strip
, .
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