Výsledky vyhledávání - "Stauffer, Allan"

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A Double Chebyshev Series: Derivation And Evaluation

Autor: Reynolds, Robert, Stauffer, Allan

In this paper we use a contour integral method to derive a generating function in the form of a double series involving the product of two Chebyshev polynomials over generalized independent indices expressed in terms of the incomplete gamma function.

Externí odkaz: http://arxiv.org/abs/2210.15485

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Sum of the Hurwitz-Lerch Zeta Function over Prime Numbers: Derivation and Evaluation

Autor: Reynolds, Robert, Stauffer, Allan

For the function $f(m,p,q,n)$, where $k,s,a$ general complex numbers and $q$ any positive integer, we establish the sum of values of the Hurwitz-Lerch zeta function $\Phi(f(m,p,q,n),k,a)$ taken at prime numbers $n$. Special cases of this sum are eval

Externí odkaz: http://arxiv.org/abs/2204.03821

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A Sextuple Integral Containing the Product of Associated Legendre polynomials $P_v^u(x) P_{\nu }^{\mu }(y)$: Derivation and Evaluation

Autor: Reynolds, Robert, Stauffer, Allan

In this present paper we derive a six dimensional integral containing the product of the Associated Legendre Polynomials $P_v^u(x) P_{\nu }^{\mu }(y)$ where the indices are different and general. Included in the kernel of this integral is the general

Externí odkaz: http://arxiv.org/abs/2201.02617

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Double integral of logarithm and exponential function expressed in terms of the Lerch function

Autor: Reynolds, Robert, Stauffer, Allan

In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double integrals

Externí odkaz: http://arxiv.org/abs/2106.03551

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Definite integrals involving combinations of powers and logarithmic functions of complicated arguments expressed in terms of the Hurwitz zeta function

Autor: Reynolds, Robert, Stauffer, Allan

In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta. These derivations are then expressed i

Externí odkaz: http://arxiv.org/abs/2103.03110

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An integral's journey over the real line

Autor: Reynolds, Robert, Stauffer, Allan

In 1826 Cauchy presented an Integral over the real line. Al and I thought a derivation would be mighty fine. So we packed our contour integral bags that day, and we now present an analytic continuation this time.
Comment: arXiv admin note: text

Externí odkaz: http://arxiv.org/abs/2103.03355

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Table in Gradshteyn and Ryzhik: Derivation of definite integrals of a Hyperbolic Function

Autor: Reynolds, Robert, Stauffer, Allan

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using

Externí odkaz: http://arxiv.org/abs/2102.12475

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