The following integral transform relationship, known as the Abel transform, exists between two functions and for ,
The Abel transform is used in calculating the radial mass distribution of galaxies (Binney and Tremaine 1987, p. 651; Arfken and Weber 2005, p. 1014) and inverting planetary radio occultation data to obtain atmospheric information as a function of height.
Bracewell (1999, p. 262) defines a slightly different form of the Abel transform given by
The following table gives a number of common Abel transform pairs (Bracewell 1999, p. 264). Here,