hyperbolic%20functions
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1: 20.10 Integrals
§20.10 Integrals
►§20.10(i) Mellin Transforms with respect to the Lattice Parameter
… ►Here again denotes the Riemann zeta function (§25.2). … ►§20.10(ii) Laplace Transforms with respect to the Lattice Parameter
… ►For corresponding results for argument derivatives of the theta functions see Erdélyi et al. (1954a, pp. 224–225) or Oberhettinger and Badii (1973, p. 193). …2: Bibliography B
3: 36.2 Catastrophes and Canonical Integrals
4: 7.8 Inequalities
5: Bibliography F
6: 36.4 Bifurcation Sets
§36.4(ii) Visualizations
…7: Bibliography M
8: Errata
Scales were corrected in all figures. The interval was replaced by and replaced by . All plots and interactive visualizations were regenerated to improve image quality.
(a) Density plot. | (b) 3D plot. |
Figure 36.3.9: Modulus of hyperbolic umbilic canonical integral function .
(a) Density plot. | (b) 3D plot. |
Figure 36.3.10: Modulus of hyperbolic umbilic canonical integral function .
(a) Density plot. | (b) 3D plot. |
Figure 36.3.11: Modulus of hyperbolic umbilic canonical integral function .
(a) Density plot. | (b) 3D plot. |
Figure 36.3.12: Modulus of hyperbolic umbilic canonical integral function .
Reported 2016-09-12 by Dan Piponi.
The scaling error reported on 2016-09-12 by Dan Piponi also applied to contour and density plots for the phase of the hyperbolic umbilic canonical integrals. Scales were corrected in all figures. The interval was replaced by and replaced by . All plots and interactive visualizations were regenerated to improve image quality.
(a) Contour plot. | (b) Density plot. |
Figure 36.3.18: Phase of hyperbolic umbilic canonical integral .
(a) Contour plot. | (b) Density plot. |
Figure 36.3.19: Phase of hyperbolic umbilic canonical integral .
(a) Contour plot. | (b) Density plot. |
Figure 36.3.20: Phase of hyperbolic umbilic canonical integral .
(a) Contour plot. | (b) Density plot. |
Figure 36.3.21: Phase of hyperbolic umbilic canonical integral .
Reported 2016-09-28.
Originally the limiting form for in the last line of this table was incorrect (, instead of ).
Reported 2010-11-23.
9: Software Index
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20 Theta Functions | |||||||||||||||||||||||||
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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.