Hankel-Hadamard determinant

Theorem 3.4 A moment set is said to be realizable if the Hankel-Hadamard determinants (Gautschi, 2004 Shohat G Tamarkin, 1943) are all non-negative ... 

It is now sufficient to modify the second-order moment to 25 (instead of 26, corresponding to a difference of only 4%) to make the moment set unrealizable. The Hankel-Hadamard determinants are now equal to -179352 and -12 362 344, respectively, whereas the difference table (see Table 3.2) presents negative elements in the column containing the second-order differences (namely A2). If this moment set is fed to the PD algorithm, the resulting quadrature is unable to reproduce the moment set. 

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