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OPM-MEG in multiple sclerosis: Proof of principle, and the effect of naturalistic posture. [PDF]

Neuroimage Clin
Sanders BJ, Gilmartin CGS, Rier L, Gascoyne L, McCann E, Cabrera J, Leggett J, Holmes N, Hill RM, Boto E, Rhodes N, Castleman C, Hibbert A, Ford DC, Schofield H, Doyle C, Osborne J, Bobela D, Shah V, Mullinger KJ, Radford K, Brookes MJ, Evangelou N.   +22 more
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p-adic Multiple Gamma Functions

p-adic Multiple Gamma Functions
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Multiple Gamma and related functions

Applied Mathematics and Computation, 2003
The authors give several new (and potentially useful) relationships between the multiple Gamma functions and other mathematical functions and constants. As by-products of some of these relationships, a classical definite integral due to Euler and other definite integrals are also considered together with closed-form evaluations of some series involving
Choi, Junesang, Srivastava, H. M., Adamchik, V. S.   +2 more
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On q-Basic Multiple Gamma Functions

International Journal of Mathematics, 2003
We define a q-analogue of the basic multiple gamma function [Formula: see text] introduced in [17] which differs from the one defined by Barnes [1] via the zeta regularized product. We call it a q-basic multiple gamma function. Using this q-basic multiple Gamma function we introduce a q-analogue of the multiple sine function of order m + 1.
Kurokawa, Nobushige, Wakayama, Masato
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Series involving the Zeta function and multiple Gamma functions

Applied Mathematics and Computation, 2004
The multiple Gamma functions were defined and studied by Barnes and by others in about 1900. Barnes gave also several explicit Weierstrass canonical product forms of the double Gamma function. By using a theorem by Dufrenoy and Pisot, in 1978 Vignéras proved a recurrence formula of the Weierstrass canonical form of the multiple Gamma function.
Choi, Junesang, Cho, Young Joon, Srivastava, H. M.   +2 more
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Multiple gamma functions, multiple sine functions, and Appell’s O-functions

The Ramanujan Journal, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Determinants of Laplacians and Multiple Gamma Functions

SIAM Journal on Mathematical Analysis, 1988
The author reinterpretes the classical formula \(\Gamma(.)=\sqrt{\pi}\) in the form \[ \Gamma(.)=2^{-1/2}(\det \Delta_ 1)^{1/4}, \] where \(\Delta_ 1=-d^ 2/dx^ 2\) denotes the Laplacian on \(S^ 1\). He then introduces so-called multiple Gamma functions \(\Gamma_ n\) for all \(n\geq 0\) and then his main result states that \(\Gamma_ n(.)\) can be ...
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On Riemann's Functional Equation with Multiple Gamma Factors

The Annals of Mathematics, 1958
(1.3) (2P7r)-isAl(s)cV(s) = (2P7Tr)4 ( S)M( S) of the following description. We have (1.4) A1(s) = F1' (p fs + Cf), (1.5) A2(S) = ll'+1 F(pS + Ce), where G > 1, H-G > 1, HG ;G. The numbers c1, * C , cH are unrestricted complex constants. The constants p1, ** , PH however are real numbers, and (1.6) PA > ?, h 1, * H (1.7) Ah + Pa + * + PHl= Actually we ...
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Functional Equations With Multiple Gamma Factors and the Average Order of Arithmetical Functions

The Annals of Mathematics, 1962
This is a further development of earlier work by the same authors [Ann. Math. (2) 74, 1--23 (1961; Zbl 0107.03702); Acta Arith. 6, 487--503 (1961; Zbl 0101.03703); C. R. Acad. Sci., Paris 251, 1333--1335 (1960; Zbl 0093.05203); erratum, p. 2547]. It is assumed that a functional equation \(\Delta(s)\varphi(s)= \Delta(\delta - s)\psi( \delta - s)\) is ...
Chandrasekharan, K., Narasimhan, Raghavan   +1 more
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