# Download e-book for iPad: An analysis of the Lanczos Gamma approximation by Pugh G.R. By Pugh G.R.

Read Online or Download An analysis of the Lanczos Gamma approximation PDF

Similar analysis books

Download e-book for kindle: Analysis and Simulation of Contact Problems by T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo

Touch mechanics used to be and is a vital department in mechanics which covers a huge box of theoretical, numerical and experimental investigations. during this rigorously edited booklet the reader will receive a state of the art evaluate on formula, mathematical research and numerical answer methods of touch difficulties.

Download e-book for iPad: Transformations Through Space and Time: An Analysis of by Daniel A. Griffith, Robert P. Haining

Lately there was a starting to be problem for the advance of either effective and potent how you can deal with space-time difficulties. Such advancements can be theoretically in addition to empirically orientated. despite which of those arenas one enters. the influence is readily received that modern wO,rk on dynamic and evolutionary versions has no longer proved to be as illuminating and profitable as first expected.

Additional resources for An analysis of the Lanczos Gamma approximation

Example text

But there are many other functions which interpolate n! between the non-negative integers; why are the standard definitions the “right” ones? The life of gamma is retraced in the very entertaining paper of Davis , according to which the year 1729 saw “the birth” of the gamma function as Euler studied the pattern 1, 1 · 2, 1 · 2 · 3, . . The problem was simple enough: it was well known that interpolating formulas of the form 1+2+···+n = n(n + 1) 2 existed for sums; was there a similar formula f (n) = 1 · 2 · · · n for products?

1 Closed Form Formulas We begin by finding explicit expressions for v and fE,r in terms of Lambert W functions W0 and W−1 . This is useful for several reasons: the first is that graphs of v and fE,r can be easily plotted using the built in Lambert W evaluation routines of Maple 8. The second is that the 52 Chapter 4. The Functions v and fE,r smoothness properties of v and fE,r can be deduced directly from those of W0 and W−1 . Third, the expression for fE,r can be used to compute approximate values of the coefficients ak (r) using finite Fourier series.

9) and recalling the infinite 28 Chapter 2. A Primer on the Gamma Function product representation of the sine function ∞ 1− sin z = z k=1 z2 k2π2 , we arrive at the very useful reflection formula Γ(1 + z)Γ(1 − z) = πz . 10) is of great practical importance since it reduces the problem of computing the gamma function at arbitrary z to that of z with positive real part. 5 Stirling’s Series and Formula Among the well known preliminary results on the gamma function, one is of particular importance computationally and requires special attention: Stirling’s series.