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Update docs with some minor corrections
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ckormanyos committed Feb 10, 2024
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The Math library provides numerous advanced mathematical functions
implemented in modern C++. The library delivers the utmost
in syntactic and numerical correctness while still
implemented in modern C++. The library strives to deliver the utmost
in numerical and syntactical correctness while still
maintaining high-performance.

All code is header-only, facilitating easy client setup
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### Special Functions

Provides a small number of high quality special functions; initially these were concentrated on functions used in statistical applications along with those in the Technical Report on C++ Library Extensions.
Provides a wide range of high quality special functions; initially these were concentrated
on functions used in statistical applications along with those in the Technical Report
on C++ Library Extensions.

The function families currently implemented are the gamma, beta & error functions along with the incomplete gamma and beta functions (four variants of each) and all the possible inverses of these, plus the digamma, various factorial functions, Bessel functions, elliptic integrals, hypergeometrics, sinus cardinals (along with their hyperbolic variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite/Chebyshev polynomials and various special power and logarithmic functions.
The function families currently implemented are the gamma, beta and error functions
along with the incomplete gamma and beta functions (four variants of each)
and all the possible inverses of these, plus the digamma, various factorial
functions, Bessel functions, elliptic integrals, hypergeometrics, sinus cardinals
(along with their hyperbolic variants), inverse hyperbolic functions,
Legrendre/Laguerre/Hermite/Chebyshev polynomials
and various special power and logarithmic functions.

All the implementations are fully generic and support the use of arbitrary "real-number" types, including Boost.Multiprecision, although they are optimised for use with types with known significand (or mantissa) sizes: typically float, double or long double.
All the implementations are fully generic and support the use of arbitrary "real-number" types,
including those in [Boost.Multiprecision](https://github.com/boostorg/multiprecision).
Most functions are, however, optimized for use with types with known significand (or mantissa) sizes:
typically built-in `float`, `double` or `long double`.

These functions also provide the basis of support for the TR1 special functions.
These functions also provide the basis of support for the TR1 special functions,
many of which became standardized in [C++17](https://en.cppreference.com/w/cpp/numeric/special_functions).

### Root Finding

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### Interpolation

Function interpolation via barycentric rational interpolation, compactly supported quadratic, cubic, and quintic B-splines, the Chebyshev transform, trigonometric polynomials, Makima, pchip, cubic Hermite splines, and bilinear interpolation.
Function interpolation via barycentric rational interpolation,
compactly supported quadratic, cubic, and quintic B-splines,
the Chebyshev transform, trigonometric polynomials, Makima,
pchip, cubic Hermite splines, and bilinear interpolation.

### Numerical Integration and Differentiation

A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre, Gauss-Kronrod, Gauss-Chebyshev, double-exponential, and Monte-Carlo) and differentiation (Chebyshev transform, finite difference, the complex step derivative, and forward-mode automatic differentiation).
A reasonably comprehensive set of routines for integration
(trapezoidal, Gauss-Legendre, Gauss-Kronrod, Gauss-Chebyshev, double-exponential, and Monte-Carlo)
and differentiation (Chebyshev transform, finite difference, the complex step derivative,
and forward-mode automatic differentiation).

The integration routines are usable for functions returning complex results - and hence can be used for computation of contour integrals.

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### Standalone Mode

Defining BOOST_MATH_STANDALONE allows Boost.Math to be used without any Boost dependencies. Some functionality is reduced in this mode. A static_assert message will alert you if a particular feature has been disabled by standalone mode.
Defining BOOST_MATH_STANDALONE allows Boost.Math to be used without any Boost dependencies.
Some functionality is reduced in this mode. A static_assert message will alert you
if a particular feature has been disabled by standalone mode.

## Supported Compilers ##

The following compilers are tested with the CI system, and are known to work. Starting with Boost 1.76 (April 2021 Release) a compiler that is fully compliant with C++11 is required to use Boost.Math.
The following compilers are tested with the CI system, and are known to work.
Currently a compiler that is fully compliant with C++14 is required to use Boost.Math.

* g++ 5 or later
* clang++ 5 or later
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