Reflection formulas for order derivatives of Bessel functions

From new integral representations of the $n$-th derivative of Bessel functions with respect to the order, we derive some reflection formulas for the first and second order derivative of $J_{\nu }\left( t\right)$ and % Y_{\nu }\left( t\right) for integral order, and for the $n$-th order derivative of $I_{\nu }\left( t\right)$ and $K_{\nu }\left( t\right)$ for arbitrary real order. As an application of the reflection formulas obtained for the first order derivative, we extend some formulas given in the literature to negative integral order. Also, as a by-product, we calculate an integral which does not seem to be reported in the literature.Comment: arXiv admin note: text overlap with arXiv:1808.0560

A note on some reduction formulas for the incomplete beta function and the Lerch transcedent

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. Also, we use these reduction formulas to test the performance of the algorithms devoted to the numerical evaluation of the incomplete beta function

Maximum Temperature in Dry Surface Grinding for High Peclet Number and Arbitrary Heat Flux Profile

Regarding heat transfer in dry surface grinding, simple asymptotic expressions of the maximum temperature for large Peclet numbers are derived. For this purpose, we consider the most common heat flux profiles reported in the literature, such as constant, linear, triangular, and parabolic. In the constant case, we provide a refinement of the expression given in the literature. In the linear case, we derive the same expression found in the literature, being the latter fitted by using a linear regression. The expressions for the triangular and parabolic cases are novel

New young planetary nebulae in IPHAS

Original article can be found at: http://www.aanda.org/ Copyright The European Southern Observatory. DOI: 10.1051/0004-6361/200811575Aims. We search for very small-diameter galactic planetary nebulae (PNe) representing the earliest phases of PN evolution. The IPHAS catalogue of H-emitting stars provides a useful basis for this study since all sources present in this catalogue must be of small angular diameter. Methods. The PN candidates are selected based on their location in two colour-colour diagrams: IPHAS (r' - H) vs. (r' - i'), and 2MASS (J - H) vs. (H - ). Spectroscopic follow-up was carried out on a sample of candidates to confirm their nature. Results. We present a total of 83 PN candidates. We were able to obtain spectra or find the classification from the literature for 35 candidates. Five of these objects are likely to be new PNe, including one large bipolar PN discovered serendipitously close to an emission-line star. PN distances deduced from extinction-distance relations based on IPHAS field-star photometry are presented for the first time. These yield distance estimates for our objects in the range 2 kpc and 6 kpc. From the data in hand, we conclude that four of the discovered objects are probably young PNe.Peer reviewe

A search for spectral hysteresis and energy-dependent time lags from X-ray and TeV gamma-ray observations of Mrk 421

Blazars are variable emitters across all wavelengths over a wide range of timescales, from months down to minutes. It is therefore essential to observe blazars simultaneously at different wavelengths, especially in the X-ray and gamma-ray bands, where the broadband spectral energy distributions usually peak. In this work, we report on three "target-of-opportunity" (ToO) observations of Mrk 421, one of the brightest TeV blazars, triggered by a strong flaring event at TeV energies in 2014. These observations feature long, continuous, and simultaneous exposures with XMM-Newton (covering X-ray and optical/ultraviolet bands) and VERITAS (covering TeV gamma-ray band), along with contemporaneous observations from other gamma-ray facilities (MAGIC and Fermi-LAT) and a number of radio and optical facilities. Although neither rapid flares nor significant X-ray/TeV correlation are detected, these observations reveal subtle changes in the X-ray spectrum of the source over the course of a few days. We search the simultaneous X-ray and TeV data for spectral hysteresis patterns and time delays, which could provide insight into the emission mechanisms and the source properties (e.g. the radius of the emitting region, the strength of the magnetic field, and related timescales). The observed broadband spectra are consistent with a one-zone synchrotron self-Compton model. We find that the power spectral density distribution at $\gtrsim 4\times 10^{-4}$ Hz from the X-ray data can be described by a power-law model with an index value between 1.2 and 1.8, and do not find evidence for a steepening of the power spectral index (often associated with a characteristic length scale) compared to the previously reported values at lower frequencies.Comment: 45 pages, 15 figure