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- [/ math.qbk
- Copyright 2006 Hubert Holin and John Maddock.
- Distributed under the Boost Software License, Version 1.0.
- (See accompanying file LICENSE_1_0.txt or copy at
- http://www.boost.org/LICENSE_1_0.txt).
- ]
- [section:sinc Sinus Cardinal and Hyperbolic Sinus Cardinal Functions]
- [section:sinc_overview Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview]
- The [@http://mathworld.wolfram.com/SincFunction.html Sinus Cardinal family of functions]
- (indexed by the family of indices [^a > 0])
- is defined by
- [equation special_functions_blurb20]
- it sees heavy use in signal processing tasks.
- By analogy, the
- [@http://mathworld.wolfram.com/SinhcFunction.htm Hyperbolic Sinus Cardinal]
- family of functions
- (also indexed by the family of indices [^a > 0]) is defined by
- [equation special_functions_blurb22]
- These two families of functions are composed of entire functions.
- These functions (__sinc_pi and __sinhc_pi) are needed by
- [@http://www.boost.org/libs/math/quaternion/quaternion.html our implementation]
- of [@http://mathworld.wolfram.com/Quaternion.html quaternions]
- and [@http://mathworld.wolfram.com/Octonion.html octonions].
- [: ['[*Sinus Cardinal of index pi (purple) and Hyperbolic Sinus Cardinal of index pi (red) on R]]]
- [: [$../graphs/sinc_pi_and_sinhc_pi_on_r.png]]
- [endsect] [/section:sinc_overview Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview]
- [section sinc_pi]
- ``
- #include <boost/math/special_functions/sinc.hpp>
- ``
- template<class T>
- ``__sf_result`` sinc_pi(const T x);
- template<class T, class ``__Policy``>
- ``__sf_result`` sinc_pi(const T x, const ``__Policy``&);
- template<class T, template<typename> class U>
- U<T> sinc_pi(const U<T> x);
- template<class T, template<typename> class U, class ``__Policy``>
- U<T> sinc_pi(const U<T> x, const ``__Policy``&);
- Computes
- [link math_toolkit.sinc.sinc_overview
- the Sinus Cardinal] of x:
- [expression sinc_pi(x) = sin(x) / x]
- The second form is for complex numbers,
- quaternions, octonions etc. Taylor series are used at the origin
- to ensure accuracy.
- [graph sinc_pi]
- [optional_policy]
- [endsect] [/section sinc_pi]
- [section sinhc_pi]
- ``
- #include <boost/math/special_functions/sinhc.hpp>
- ``
- template<class T>
- ``__sf_result`` sinhc_pi(const T x);
- template<class T, class ``__Policy``>
- ``__sf_result`` sinhc_pi(const T x, const ``__Policy``&);
- template<typename T, template<typename> class U>
- U<T> sinhc_pi(const U<T> x);
- template<class T, template<typename> class U, class ``__Policy``>
- U<T> sinhc_pi(const U<T> x, const ``__Policy``&);
- Computes [@http://mathworld.wolfram.com/SinhcFunction.html sinhc function],
- the [link math_toolkit.sinc.sinc_overview Hyperbolic Sinus Cardinal] of x:
- [expression sinhc_pi(x) = sinh(x) / x]
- The second form is for
- complex numbers, quaternions, octonions etc. Taylor series are used at the origin
- to ensure accuracy.
- The return type of the first form is computed using the __arg_promotion_rules
- when T is an integer type.
- [optional_policy]
- [graph sinhc_pi]
- [endsect] [/section sinhc_pi]
- [endsect] [/section:sinc Sinus Cardinal and Hyperbolic Sinus Cardinal Functions]
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