PURUSPE

PURe RUSt SPEcial function library. There are no dependencies.

Implemented Functions

Gamma functions

• ln_gamma : Logarithmic gamma function
• gamma : Gamma function
• gammp : Regularized lower gamma function
• gammq : Regularized upper gamma function
• invgammp : Inverse regularized lower gamma function

Beta function

• beta : Beta function
• betai : Regularized Incomplete beta function
• invbetai : Inverse regularized incomplete beta function

Error functions

• erf : Error function
• erfc : Complementary Error function
• inverf : Inverse error function
• inverfc : Inverse complementary error function

Bessel functions

• Jn : Bessel function of the first kind (integer order)
• Yn : Bessel function of the second kind (integer order)
• In : Modified Bessel function of the first kind (integer order)
• Kn : Modified Bessel function of the second kind (integer order)
• Jnu_Ynu : Bessel function of the first kind and second kind (fractional order)
• Inu_Knu : Modified Bessel function of the first kind and second kind (fractional order)
• besseljy : Bessel function of the first and second kinds (include derivatives)
• besselik : Modified Bessel function of the second kind (include derivatives)

Dawson's integral

• dawson: Dawson's integral

Note on precision of Bessel functions

Bessel functions exhibit poor precision for extremely large arguments. For instance, Jn(1,1e10) yields only 6 correct digits, in contrast to the typical 14 digits of double precision. This behavior is comparable to Python's scipy.special.j1, which is an optimized variant of the Bessel J function.

Reference

• Press, William H., and William T. Vetterling. Numerical Recipes. Cambridge: Cambridge Univ. Press, 2007.