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Some implications of a new definition of...

Cieslinski, Jan L....

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Some implications of a new definition of the exponential function on time scales by Cieslinski, Jan L. ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	29-08-2010
Summary	We present a new approach to exponential functions on time scales and to timescale analogues of ordinary differential equations. We describe in detail the Cayley-exponential function and associated trigonometric and hyperbolic functions. We show that the Cayley-exponential is related to implicit midpoint and trapezoidal rules, similarly as delta and nabla exponential functions are related to Euler numerical schemes. Extending these results on any Pad\'e approximants, we obtain Pad\'e-exponential functions. Moreover, the exact exponential function on time scales is defined. Finally, we present applications of the Cayley-exponential function in the q-calculus and suggest a general approach to dynamic systems on Lie groups.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	https://arxiv.org/abs/1008.4911

Citation

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AMA 11th EditionReferences

Cieslinski, Jan L.. Some implications of a new definition of the exponential function on time scales. N.A. August 29, 2010. Accessed October 03, 2025. https://online.provdatabase.com/cite/12720

APA 7th EditionReferences

Cieslinski, Jan L.. (2010). Some implications of a new definition of the exponential function on time scales. N.A. https://online.provdatabase.com/cite/12720

Chicago 17th EditionReferences

Cieslinski, Jan L.. Some implications of a new definition of the exponential function on time scales. N.A. 2010. https://online.provdatabase.com/cite/12720

HarvardReferences

Cieslinski, Jan L.. (2010). Some implications of a new definition of the exponential function on time scales. [Online]. N.A. Available from: https://online.provdatabase.com/cite/12720. (Accessed 03 October 2025).

Harvard AustraliaReferences

Cieslinski, Jan L., 2010, Some implications of a new definition of the exponential function on time scales, N.A, viewed 03 October 2025, <https://online.provdatabase.com/cite/12720>

MLA 9th EditionWorks Cited

Cieslinski, Jan L.. Some implications of a new definition of the exponential function on time scales. N.A, 2010. PROV Database, https://online.provdatabase.com/cite/12720.

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