# 1. Mathematical Functions and Differential Equations[-]

Mathematical Functions
• The Airy function of the first kind $$ $$
• The Airy function of the second kind $$ $$
• The Anger function $$ $$
• The inverse cosine $$ $$
• The inverse hyperbolic cosine $$ $$
• The inverse cotangent $$ $$
• The inverse hyperbolic cotangent $$ $$
• The inverse cosecant $$ $$
• The inverse hyperbolic cosecant $$ $$
• The inverse secant $$ $$
• The inverse hyperbolic secant $$ $$
• The inverse sine $$ $$
• The inverse hyperbolic sine $$ $$
• The inverse tangent $$ $$
• The inverse hyperbolic tangent $$ $$
• The modified Bessel function of the first kind $$ $$
• The Bessel function of the first kind $$ $$
• The modified Bessel function of the second kind $$ $$
• The Bessel function of the second kind $$ $$
• The Chebyshev function of the first kind $$ $$
• The Chebyshev function of the second kind $$ $$
• The hyperbolic cosine integral $$ $$
• The cosine integral $$ $$
• The cosine $$ $$
• The hyperbolic cosine $$ $$
• The Coulomb function $$ $$
• The Whittaker's parabolic function $$ $$
• The parabolic cylinder function $$ $$
• The parabolic cylinder function $$ $$
• The differentiated Airy function of the first kind $$ $$
• The differentiated Airy function of the second kind $$ $$
• The Dawson integral $$ $$
• The dilogarithm $$ $$
• The exponential integral $$ $$
• The complementary complete elliptic integral of the second kind $$ $$
• The complementary complete elliptic integral of the first kind $$ $$
• The complete elliptic integral of the second kind $$ $$
• The incomplete elliptic integral of the second kind $$ $$
• The incomplete elliptic integral of the second kind $$ $$
• The incomplete elliptic integral of the first kind $$ $$
• The incomplete elliptic integral of the first kind $$ $$
• The complete elliptic integral of the first kind $$ $$
• The error function $$ $$
• The complementary error function $$ $$
• The iterated integral of the complementary error function $$ $$
• The imaginary error function $$ $$
• The exponential $$ $$
• The Gegenbauer ultraspherical function $$ $$
• The Hermite function $$ $$
• The Jacobi function $$ $$
• The Kummer function $$ $$
• The Kummer function $$ $$
• The Laguerre function $$ $$
• The associated Legendre function of the first kind $$ $$
• The associated Legendre function of the second kind $$ $$
• The logarithm $$ $$
• The Lommel function $$ $$
• The Lommel function $$ $$
• The hyperbolic sine integral $$ $$
• The sine integral $$ $$
• The sine $$ $$
• The hyperbolic sine $$ $$
• The shifted sine integral $$ $$
• The Struve function $$ $$
• The Struve function $$ $$
• The Weber function $$ $$
• The Whittaker function $$ $$
• The Whittaker function $$ $$
Welcome to this interactive site on Mathematical Functions, with properties, truncated expansions, numerical evaluations, plots, and more. The functions currently presented are elementary functions and special functions of a single variable. More functions — special functions with parameters, orthogonal polynomials, sequences — will be added with the project advances.
This is release 1.9.1 of DDMF
Select a special function from the list
What's new? The main changes in this release 1.9.1, dated May 2013, are:
• Proofs related to Taylor polynomial approximations.
Release history.
More on the project: The DDMF project (2008–2013) is hosted and supported by the Microsoft Research – INRIA Joint Centre.