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Date: 24-12-2020
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Date: 17-9-2020
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Date: 12-12-2020
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By analogy with the sinc function, define the sinhc function by
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(1) |
Since is not a cardinal function, the "analogy" with the sinc function is one of functional structure, not mathematical properties. It is quite possible that a better term than
could be coined, although there appears to be no other name previously assigned to this function.
The function has derivative
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(2) |
and indefinite integral
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(3) |
where is the Shi function.
The function has real fixed points at 1.31328371835... (OEIS A133916) and 2.63924951389... (OEIS A133917).
REFERENCES:
Holin, H. "C++ Boost Special Functions Library." https://www.boost.org/doc/libs/1_46_1/boost/math/special_functions/sinhc.hpp.
Sloane, N. J. A. Sequences A133916 and A133917 in "The On-Line Encyclopedia of Integer Sequences."
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