The mystery of the shape parameter IV

This is the fourth paper of our study of the shape parameter c   contained in the famous multiquadrics (−1)⌈β⌉(c2+‖x‖2)β,β>0, and the inverse multiquadrics (c2+‖x‖2)β,β<0. The theoretical ground is the same as the third paper. However, we extend the space of interpolated functions to a more general one. This leads to a totally different set of criteria of choosing c.