The fundamental ERI and the basis of all ERI algorithms is usually represented[Gill(1994)]

(B.3) | |||||

(B.4) |

which can be reduced to a one-dimensional integral of the form

(B.5) |

and can be efficiently computed using a modified Chebyshev interpolation scheme.[Gill et al.(1991)Gill, Johnson, and Pople] Equation eq:b4 can also be adapted for the general case integrals required for most calculations. Following the fundamental ERI, building up to the full bra-ket ERI (or intermediary matrix elements, see later) are the problems of angular momentum and contraction.

**Note: **Square brackets denote primitive integrals and parentheses denote fully-contracted integrals.