with imaginary periods
(0.004 seconds)
11—20 of 40 matching pages
11: 28.12 Definitions and Basic Properties
…
►
28.12.6
…
12: About Color Map
…
►For the continuous phase mapping, we map the phase continuously onto the hue, as both are periodic.
In doing this, however, we would like to place the mathematically significant phase values, specifically the multiples of correponding to the real and imaginary axes, at more immediately recognizable colors.
…
►
…
13: 29.12 Definitions
…
►
…
14: 21.3 Symmetry and Quasi-Periodicity
…
►
21.3.3
…
15: 25.1 Special Notation
…
►
►
…
►The main related functions are the Hurwitz zeta function , the dilogarithm , the polylogarithm (also known as Jonquière’s function ), Lerch’s transcendent , and the Dirichlet -functions .
nonnegative integers. | |
… | |
complex variable. | |
complex variable. | |
… | |
periodic Bernoulli function . | |
… |
16: 28.29 Definitions and Basic Properties
…
►
is the minimum period of .
…
►where the function is -periodic.
…
►The solutions of period
or are exceptional in the following sense.
If (28.29.1) has a periodic solution with minimum period
, , then all solutions are periodic with period
.
…
17: 20.2 Definitions and Periodic Properties
§20.2 Definitions and Periodic Properties
… ►§20.2(ii) Periodicity and Quasi-Periodicity
►For fixed , each is an entire function of with period ; is odd in and the others are even. … ►The theta functions are quasi-periodic on the lattice: … ►§20.2(iii) Translation of the Argument by Half-Periods
…18: 29.17 Other Solutions
…
►
29.17.1
…
►They are algebraic functions of , , and , and have primitive period
.
…
►Lamé–Wangerin functions are solutions of (29.2.1) with the property that is bounded on the line segment from to .
…
19: 28.33 Physical Applications
…
►
•
…
►with , reduces to (28.32.2) with .
…The separated solutions must be -periodic in , and have the form
…
►If the parameters of a physical system vary periodically with time, then the question of stability arises, for example, a mathematical pendulum whose length varies as .
…
►For points that are at intersections of with the characteristic curves or , a periodic solution is possible.
…