Special Functions in MATLAB

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1. sin calculates sine of arguments in radian while sind calculates sine of arguments in degrees; asin calculates inverse of sine resulting in radian while asind calculates inverse of sine resulting in degrees. Other triangular functions behave similarly.

2. The modified Bessel function of the first kind $I_n(x)$ is implemented as besseli in MATLAB. Notice that for large value x, $I_n(x)$ is huge, so it is better to use scaled Bessel function for large x. To do this, you just need specify an extra argument for besseli. Notice that other kind of Bessel functions are also implemented in MATLAB.

3. Incomplete Beta function is implemented as betainc and incomplete Gamma function is implemented as gammainc in MATLAB.

4. The logarithm of Gamma function is implemented as gammaln and the logarithm of Beta function is implemented as betaln in MATLAB.

5. cart2sph, cart2pol, pol2crt, sph2cart, hsv2rgb and rgb2hsv can transform coordinates between different coordinate systems.

6. mfun can help evaluate special mathematica functions numerically, but you should be aware of the fact that the result return by calling mfun is not as accurate as invoking these special function directly in MATLAB, especially when a function is near its root and its arguments are relatively large. Also mfunlist can list special functions for use with mfun.