ZETA functionsWe define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck–Witt group. We show that this enrichment is related to the topology of the real points of a lift. For cell...
For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the tool,we obtain with ease an expression for T(s,s...
In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivat...
I want to write the prime of this hankel function expansion, where , zeta, B0, ka are given, nu is complex which is also given in the question, How can I write the derivatiove of this Hankel function first kind equation 21? I am providing here the equa...
Fernandez, A., Djida, J.D.: Fractional differential relations for the Lerch zeta function. Arch. Math. (Basel) 117(5), 515–527 (2021) Article MathSciNet Google Scholar Gavrea, I., Ivan, M.: An inequality for continuous linear functionals. Appl. Math. Lett. 23(4), 381–384 (20...
Taking further derivatives of eq. (7) then yields: ψ (n) (x) = d n+1 ln Γ(x) dx n+1 = (−1) n+1 n! ∞ k=0 1 (x +k) n+1 , n = 1, 2, 3, . . . If we set x = 1, then using the definition of the Riemann zeta function: ζ(n) = ∞ k=0 1 (k...
Interestingly, the absorption-enhancing effects of the protein-PAMAM dendrimers are linearly correlated with the positive charge of the protein-PAMAM dendrimers which is determined by their zeta potential. Enoxaparin–G2-(or G3)-PAMAM dendrimer complex is effective in preventing deep vein throm...
They can be found at each order of \alpha ', up to overall factors, by imposing the effective action at that order to be invariant under the O(1, 1) symmetry. Hence, the T-duality constraint can not predict the overall factors a_1,\zeta (3),a_1\zeta (3),a_1^2\zeta (3),\...
ZetaOfThree Thread Aug 9, 2014 Derivative Feynman Feynman lectures Lectures Second derivative Unit Unit vector Vector Replies: 1 Forum: General Math S Derivative of a rotating unit vector I think this is a textbook-style question, if I am wrong, please redirect me to the forum section wh...
Using generalized zeta function regularization, we first note that h2 has dimension d − 1 − 2∆q, and we rewrite the log − ∞ degG( =0 ) log(µd−1−2∆q λ(k,q)( )) = d ds ∞ degG( =0 )(µd−1−2∆q λ(k,q)( ))−s , s=0 (4.38) where ...