Published August 7, 2024 | Version v2
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Boys' Function Computed by Gauss-Jacobi Quadrature

  • 1. Max-Planck Institute of Astronomy

Description

Boys' Function F_m(z) that appears in the quantum mechanics of Gaussian Type 
Orbitals is a special case of Kummer's confluent hypergeometric function. 
We evaluate its integral representation of a product of a power and an 
exponential function over the unit interval with the numerical Gauss-Jacobi 
quadrature. 

We provide a C function boysGaussJacobi(int m, double z) for real positive values
of the argument z which basically employs a table of the weights and abscissae 
of the quadrature rule for integer quantum numbers m<= 129 copied from

https://vixra.org/abs/1709.0304

We provide a C function boysGaussJacobiC(int m, complex double z) for complex 
values which uses a lookup table on a grid of reference values of z as detailed 
in https://doi.org/10.1023/B:NUMA.0000040063.91709.58 .

[https://zenodo.org/records/3603249]

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Is part of
Preprint: http://vixra.org/abs/1709.0304 (URL)

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