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==Coefficients==
The coefficients are given by
:<math>p_k(g) = \frac{\sqrt{2\,}}{\pi} \sum_{a\ell=0}^k C(C_{2k+1, 2a+1) \frac{\sqrt{,2}}{\piell+1} \left(a\ell - \tfrac12tfrac{1}{2} \right)! {\left(a\ell + g + \tfrac12tfrac{1}{2} \right)}^{- \left( a\ell + \frac12tfrac{1}{2} \right) } e^{a\ell + g + \frac12 }</math>
withwhere ''C''(''i''<math>C_{n,m}</math> ''j'') denotingrepresents the (''in'', ''jm'')th element of the [[Chebyshevmatrix polynomial(mathematics)|matrix]] coefficientof coefficients for the [[matrixChebyshev (mathematics)|matrixpolynomial]]s, which can be calculated [[recursion|recursively]] from thethese identities:
:<math>\begin{align}
C( C_{1,\,1)} &= 1 \\[5px]
C( C_{2,\,2)} &= 1 \\[5px]
C(i C_{n+1,\,1)} &= -C(i\,C_{n-21,\, 1)} & i\text{ for } n &= 2, 3, 4\, \dots \\[5px]
C(iC_{n+1,j)\,n+1} &= 2 C(i-1\,C_{n,\,n} j-1) & i &= j\text{ for } n &= 2, 3, 4\, \dots \\[5px]
C(iC_{n+1,j)\,m+1} &= 2\,C_{n,\,m} C(i-1, jC_{n-1),\,m+1} -& C(i-2,\text{ j)for & i} n & > jm = 1, 2, 3\, \dots
\end{align}</math>
PaulGodfrey Godfrey(2001) describes how to obtain the coefficients and also the value of the truncated series ''A'' as a [[matrix multiplication|matrix product]].<ref name=Godfrey2001>{{cite web |last=Godfrey |first=Paul |year=2001 |title=Lanczos implementation of the gamma function |url=http://www.numericana.com/answer/info/godfrey.htm |website=Numericana}}</ref>
==Derivation==
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