# 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 mathematical rendering to enable access to the contents
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.