Highly accurate evaluation of the few-body auxiliary functions and four-body integrals

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Abstract
Analytical formulae suitable for numerical calculations of the second- and third-order auxiliary functions A2(k,m,a,b) and A3(k ,� , m,a,b,c) are presented. These formulae can directly be used in highly accurate calculations of the A2(k,m,a,b) and A3(k ,� , m,a,b,c) functions. In turn, the highly accurate auxiliary functions of the second and third order are used to compute various four-body integrals, fourth-order auxiliary functions A4(k ,� , m,n,a,b,c,d) and so-called general four-body integrals. The A2(k,m,a,b) and A3(k ,� , m,a,b,c) functions can be used to solve a large number of four-, five- and many-body problems from atomic, nuclear and molecular physics.