Lanczos approximation: Difference between revisions

Revision as of 22:24, 21 December 2015

Revision as of 22:26, 21 December 2015

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:<math>A_g(z) = \frac{1}{2}p_0(g) + p_1(g) \frac{z}{z+1} + p_2(g) \frac{z(z-1)}{(z+1)(z+2)} + \cdots.</math>

Here ''g'' is a [[Constant (mathematics)|constant]] that may be chosen arbitrarily subject to the restriction that Re(''z'') > 1/2.<ref>[https://web.viu.ca/pughg/phdThesis/phdThesis.pdf#110 Pugh thesis] (page 101) </ref> The coefficients ''p'', which depend on ''g'', are slightly more difficult to calculate (see below). Although the formula as stated here is only valid for arguments in the right complex [[half-plane]], it can be extended to the entire [[complex plane]] by the [[reflection formula]],

:<math>\Gamma(1-z) \; \Gamma(z) = {\pi \over \sin \pi z}.</math>