For the Neumann problem in B + and B − the formulae are due to Neumann and Bjerknes, respectively. If we consider the stationary heat conduction, and B + or B − by means of a plane through the centre of B + is divided into two domains with different heat flux constants, then ...
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If the order of the at least used difference in even, it also can be shown that a further improvement is not possible; in case of odd order this is still valid with regard to the significant part, i. e. the more slowly with the steplength against zero converging part of the ...
The remainder terms of quadrature formulas expressed in the exact form of integrals are deduced in a most simple manner. Derivatives of the approximately integrated function of an arbitrary order and the periodic Bernoulli's functions are contained in these remainder terms....