Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509665 | Journal of Computational and Applied Mathematics | 2005 | 9 Pages |
Abstract
It is well known that the polygamma functionsΨk(z)âdk+1dzk+1LogÎ(z),k=0,1,2,â¦can be represented in the half-plane region |argz|<Ï/2 by Stieltjes continued fractionsg(k,z)=a1(k)z2+a2(k)1+a3(k)z2+a4(k)1+â¯,am(k)>0.In the present paper it is shown that the coefficients am(k) have the asymptotic behavioram(k)â¼m216,mââ.From this it is deduced that the nth approximant gn(k,z) of g(k,z) converges at the rate|g(k,z)-gn(k,z)|⩽AnB,n⩾1,where the positive constants A and B depend upon k and z, but are independent of n.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Catherine M. Bonan-Hamada, William B. Jones,