Polylogarithm function li
WebPolylogarithm Function Description. Computes the n-based polylogarithm of z: Li_n(z). Usage polylog(z, n) Arguments. z: real number or vector, all entries satisfying abs(z)<1. n: … WebJun 30, 2024 · Various methods are used to investigate sums involving a reciprocal central binomial coefficient and a power term. In the first part, new functions are introduced for calculation of sums with a negative exponent in the power term. A recurrence equation for the functions provides an integral representation of the sums using polylogarithm …
Polylogarithm function li
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WebThis paper extends tools developed by Crandall (2012) 16 to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta ... Webapplications in analyzing lower order terms in the behavior of zeros of L-functions near the central point. 1. INTRODUCTION The polylogarithm function Lis(x) is Lis(x) = X1 k=1 …
WebPolylogarithms. This implements the Polylogarithm and some related functions that were needed (Harmonic numbers, Stieltjes constants, and Bernoulli numbers and polynomials). … WebIt appears that the only known representations for the Riemann zeta function ((z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ((n) for any integer n > 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n > 1, by using the …
WebOct 24, 2024 · In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li s (z) of order s and argument z.Only for special … WebPolylogarithm and Geometric Progression. Polylogarithm is connected to the infinite geometric progression sum \operatorname {Li}_0 (x)=\sum_ {n=1}^\infty x^n=\dfrac {x} {1 …
WebWe give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing new results and further reinforcing the well-known connection between Euler sums and …
WebThis function is defined in analogy with the Riemann zeta function as providing the sum of the alternating series. η ( s) = ∑ k = 0 ∞ ( − 1) k k s = 1 − 1 2 s + 1 3 s − 1 4 s + …. The eta … can i put 22 1/2 tires on 19 1/2 on my rvWebxm Liq ( x) Lit ( x)dx, Z1 0 1 x Liq ( x) Lit x2 dx, for m 2, and for integers q and t. For m = 2, 1,0, we give explicit representations of the integrals in terms of Euler sums. For the case R1 0 … can i put 2 amazon returns in 1 boxWebThe functions Lin(z) are de ned on Cpnf1g. If Lis a nitely rami ed extension of Qpthen the limit limz!1 z2L Lin(z) exists for n 2, and is independent of L. Using this limit as the value for Lin at 1, Lin extends to a function on Cp, which is continuous on nitely rami ed extensions of Qp. If mand nare integers at least equal to 2, then on Cp can i put 2 3/4 shells in a 3 inch chamberWebThe polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit … five in a row mini unitWebBoundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. As main results, this … can i put 17 rims on a 20 rim carWebThe code is aimed at calculating Li_s(z) for all (complex) s and z. This is still a little experimental, but there is a fairly large test set that all works nicely. Note that the aimed … five-in-a-row gamecan i put 2 cycle oil in my push mower