On the Barnes double zeta and Gamma functions

We present a complete description of the analytic properties of the Barnes double zeta and Gamma functions. (C) 2009 Elsevier Inc. All rights reserved.

A note on a gamma distribution computer program and computer produced graphs /

"NOAA--S/T 77-2535"

A note on a gamma distribution computer program /

Mode of access: Internet.

Théorie de la fonction gamma.

Available on demand as hard copy or computer file from Cornell University Library.

La fonction gamma: théorie, histoire, bibliographie,

Available on demand as hard copy or computer file from Cornell University Library.

Series representations of the remainders in the expansions for certain functions with applications

We present a summary of the series representations of the remainders in the expansions in ascending powers of t of 2/(et+1)2/(et+1) , sech t and coth t and establish simple bounds for these remainders when t>0t>0 . Several applications of these expansions are given which enable us to deduce some inequalities and completely monotonic functions associated with the ratio of two gamma functions. In addition, we derive a (presumably new) quadratic recurrence relation for the Bernoulli numbers Bn.

Modeling of the hemodynamic responses in block design fMRI studies

The hemodynamic response function (HRF) describes the local response of brain vasculature to functional activation. Accurate HRF modeling enables the investigation of cerebral blood flow regulation and improves our ability to interpret fMRI results. Block designs have been used extensively as fMRI paradigms because detection power is maximized; however, block designs are not optimal for HRF parameter estimation. Here we assessed the utility of block design fMRI data for HRF modeling. The trueness (relative deviation), precision (relative uncertainty), and identifiability (goodness-of-fit) of different HRF models were examined and test-retest reproducibility of HRF parameter estimates was assessed using computer simulations and fMRI data from 82 healthy young adult twins acquired on two occasions 3 to 4 months apart. The effects of systematically varying attributes of the block design paradigm were also examined. In our comparison of five HRF models, the model comprising the sum of two gamma functions with six free parameters had greatest parameter accuracy and identifiability. Hemodynamic response function height and time to peak were highly reproducible between studies and width was moderately reproducible but the reproducibility of onset time was low. This study established the feasibility and test-retest reliability of estimating HRF parameters using data from block design fMRI studies.

Exact energy eigenvalues for an attractive Coulomb potential with zero-radius hard core

Following a peratization procedure, the exact energy eigenvalues for an attractive Coulomb potential, with a zero-radius hard core, are obtained as roots of a certain combination of di-gamma functions. The physical significance of this entirely new energy spectrum is discussed.

Massless scattering at special kinematics as Jacobi polynomials

We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two-parameter family of kinematics. We present explicit and compact formulas for the n-gluon and n-graviton partial scattering amplitudes for our special kinematics in terms of Jacobi polynomials. We also provide alternative expressions in terms of gamma functions. We give an interpretation of the common reduced determinant appearing in the amplitudes as the product of the squares of the eigenfrequencies of small oscillations of a system whose equilibrium is the solutions of the scattering equations.

Comparison of pattern VEP results acquired using CRT and TFT stimulators in the clinical practice

There are several electrophysiological systems available commercially. Usually, control groups are required to compare their results, due to the differences between display types. Our aim was to examine the differences between CRT and LCD/TFT stimulators used in pattern VEP responses performed according to the ISCEV standards. We also aimed to check different contrast values toward thresholds. In order to obtain more precise results, we intended to measure the intensity and temporal response characteristics of the monitors with photometric methods. To record VEP signals, a Roland RetiPort electrophysiological system was used. The pattern VEP tests were carried out according to ISCEV protocols on a CRT and a TFT monitor consecutively. Achromatic checkerboard pattern was used at three different contrast levels (maximal, 75, 25%) using 1A degrees and 15` check sizes. Both CRT and TFT displays were luminance and contrast matched, according to the gamma functions based on measurements at several DAC values. Monitor-specific luminance parameters were measured by means of spectroradiometric instruments. Temporal differences between the displays` electronic and radiometric signals were measured with a device specifically built for the purpose. We tested six healthy control subjects with visual acuity of at least 20/20. The tests were performed on each subject three times on different days. We found significant temporal differences between the CRT and the LCD monitors at all contrast levels and spatial frequencies. In average, the latency times were 9.0 ms (+/- 3.3 ms) longer with the TFT stimulator. This value is in accordance with the average of the measured TFT input-output temporal difference values (10.1 +/- A 2.2 ms). According to our findings, measuring the temporal parameters of the TFT monitor with an adequately calibrated measurement setup and correcting the VEP data with the resulting values, the VEP signals obtained with different display types can be transformed to be comparable.

Compendium der höheren analysis.

v. 2 has added t.-p.: "Vorlesungen über einzelne theile der höheren analysis" 3. aufl. 1879.

G. Lejeune-Dirichlets Vorlesungen über die Lehre von den Einfachen und Mehrfachen bestimmten Integralen.

Available on demand as hard copy or computer file from Cornell University Library.

Sur l'intégrale eulérienne de première espèce.

"Extrait du t. LIII des Mémoires couronnées et Mémoires des savants étrangers, pub. par l'Académie royale des sciences, des lettres et des beaux-arts de Belgique, 1893."

Vorlesungen über die Lehre von den einfachen und mehrfachen bestimmten Integralen /

Preservation photocopy on alkaline paper.

Improving CAS Capabilities: New Rules for Computing Improper Integrals

There are diferent applications in Engineering that require to compute improper integrals of the first kind (integrals defined on an unbounded domain) such as: the work required to move an object from the surface of the earth to in nity (Kynetic Energy), the electric potential created by a charged sphere, the probability density function or the cumulative distribution function in Probability Theory, the values of the Gamma Functions(wich useful to compute the Beta Function used to compute trigonometrical integrals), Laplace and Fourier Transforms (very useful, for example in Differential Equations).