Results 11 to 20 of about 148 (36)
The resurgence properties of the incomplete gamma function I [PDF]
, 2014 In this paper we derive new representations for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396).
Nemes, Gergő
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A note on some reduction formulas for the incomplete beta function and the Lerch transcedent [PDF]
, 2020 We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals.
González-Santander, J. L.
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A generalisation of an expansion for the Riemann zeta function involving incomplete gamma functions [PDF]
, 2009 We derive an expansion for the Riemann zeta function ζ(s) involving incomplete gamma functions with their second argument proportional to n2p, where n is the summation index and p is a positive integer.
Paris, Richard B.
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Some special functions identities arising from commuting operators
, 2008 Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of order $k$ and the
Abramowitz +8 more
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Inverse hyperbolic equation, Spectral technique, Regularization method, Operational matrix
Kuwait Journal of ScienceRecently, the realm related to Euler's Beta function has played a significant role in the development of special function theory. In this study, a new extension of the special function known as Euler's Beta function with respect to the Mittag-Leffler ...
Firas Ghanim +2 more
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, 2009 A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely monotonic.
Guo, Bai-Ni, Qi, Feng
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, 2015 This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0, that allow for different orders and arguments in the two parabolic ...
Veestraeten, Dirk
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Some integral representations and limits for (products of) the parabolic cylinder function
, 2015 Veestraeten [1] recently derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting the link between the parabolic cylinder function and the transition density and distribution ...
Veestraeten, Dirk
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An asymptotic expansion for the error term in the Brent-McMillan algorithm for Euler’s constant [PDF]
, 2019 The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler’s constant γ and is based on the modified Bessel functions I_0(2x) and K_0(2x). An error estimate for this algorithm relies on the optimally truncated
Paris, R. B.
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Solution to an open problem on a logarithmic integral and derived results
Annals of the West University of Timisoara: Mathematics and Computer ScienceThis article solves an open problem that was previously stated by providing an exact evaluation of a logarithmic integral. Furthermore, the result is generalized by introducing a new adjustable parameter.
Coine Clément, Chesneau Christophe
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