Abstract
In this paper we investigate the representation of integrals involving the product of the Legendre Chi function, polylogarithm function and log function. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet Eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.
Highlights
Anthony SofoIn this paper we investigate the representation of integrals involving the product of the Legendre Chi function, polylogarithm function and log function
PRELIMINARIES AND NOTATIONIn this paper we investigate the representations of integrals of the type (1)xaχp (x) Liq(δxb) lnm (x) dx, in terms of special functions such as zeta functions, Dirichlet eta functions, polylogarithmic functions, beta functions and others
It is known that the Lerch transcendent extends by analytic continuation to a function Φ (z, t, a) which is defined for all complex t, z ∈ C − [1, ∞) and a > 0, which can be represented, [15], by the integral formula xt−1e−(t−1)x
Summary
In this paper we investigate the representation of integrals involving the product of the Legendre Chi function, polylogarithm function and log function.
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