Zeldovich regularization

Zeldovich regularization refers to a regularization method to calculate divergent integrals and divergent series, that was first introduced by Yakov Zeldovich in 1961.^[1] Zeldovich was originally interested in calculating the norm of the Gamow wave function which is divergent since there is an outgoing spherical wave. Zeldovich regularization uses a Gaussian type-regularization and is defined, for divergent integrals, by^[2]

${\displaystyle \int _{0}^{\infty }f(x)dx\equiv \lim _{\alpha \to 0^{+}}\int _{0}^{\infty }f(x)e^{-\alpha x^{2}}dx.}$

and, for divergent series, by^[3][4][5]

${\displaystyle \sum _{n}c_{n}\equiv \lim _{\alpha \to 0^{+}}\sum _{n}c_{n}e^{-\alpha n^{2}}.}$

See also

• Abel's theorem
• Borel summation