change of modulus
(0.004 seconds)
31—40 of 92 matching pages
31: 15.12 Asymptotic Approximations
32: 19.2 Definitions
33: 2.11 Remainder Terms; Stokes Phenomenon
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βΊIn the transition through ,
changes very rapidly, but smoothly, from one form to the other; compare the graph of its modulus in Figure 2.11.1 in the case .
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34: 2.4 Contour Integrals
35: 7.7 Integral Representations
36: 28.12 Definitions and Basic Properties
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βΊFor change of signs of and ,
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βΊFor changes of sign of , , and ,
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βΊ
28.12.9
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βΊWhen is a rational number, but not an integer, all solutions of Mathieu’s equation are periodic with period .
βΊFor change of signs of and ,
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37: 23.21 Physical Applications
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βΊ
23.21.3
βΊAnother form is obtained by identifying , , as lattice roots (§23.3(i)), and setting
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βΊ
23.21.5
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38: 2.3 Integrals of a Real Variable
39: 25.10 Zeros
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βΊBecause , vanishes at the zeros of , which can be separated by observing sign changes of .
Because
changes sign infinitely often, has infinitely many zeros with real.
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βΊBy comparing with the number of sign changes of we can decide whether has any zeros off the line in this region.
Sign changes of are determined by multiplying (25.9.3) by to obtain the Riemann–Siegel formula:
…where as .
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