Derivation of filter tables
Most of these classic tables come from the work of Wilhelm Cauer on network synthesis. Such filters are known as Cauer Networks or Cauer Ladders as a result of this work. There is also the Cauer filter which is a special case of such a network. A good book on circuit theory should cover some of this and, if I remember correctly, it involves long division of Laplace polynomials (generalized continued fractions) - not for the faint hearted!