Daubechies wavelet

Daubechies wavelets are a family of orthogonal wavelets named after Belgian physicist and mathematician Ingrid Daubechies. They are used in discrete wavelet transform.
Definition.
Scale function coefficients (low pass filter in orthogonal filter banks) must satisfy following conditions (formula_1 is length of filter).
which implies
There is more than one solution (except case of formula_12). However, it is necessary to distinguish between low pass and high pass filter.
Wavelets are denoted like D"x", where "x" is either number of coefficients (formula_1) or number of vanishing moments (formula_14). First case of notation (number of coefficients) is more recent and more frequented (e.g. D8 is wavelet with 8 coefficients).
Example.
MATLAB code for enumeration of wavelet with 4 coefficients (denoted as D4).
t = solve(
 'h0*h0 + h1*h1 + h2*h2 + h3*h3 = 1', % normalization
 'h2*h0 + h3*h1 = 0', % orthogonality
 '+(0^0)*h0 -(1^0)*h1 +(2^0)*h2 -(3^0)*h3 = 0', % zero
 '+(0^1)*h0 -(1^1)*h1 +(2^1)*h2 -(3^1)*h3 = 0' % and first vanishing moments
Solutions (low pass filters only):