Results 281 to 290 of about 549,355 (294)

Integrating single-cell RNA and T cell/B cell receptor sequencing with mass cytometry reveals dynamic trajectories of human peripheral immune cells from birth to old age. [PDF]

Nat Immunol
Wang Y, Li R, Tong R, Chen T, Sun M, Luo L, Li Z, Chen Y, Zhao Y, Zhang C, Wei L, Lin W, Chen H, Qian K, Chen AF, Liu J, Chen L, Li B, Wang F, Wang L, Su B, Pu J.   +21 more
europepmc   +1 more source

Islet single-cell transcriptomic profiling during obesity-induced beta cell expansion in female mice. [PDF]

iScience
Masschelin PM, Ochsner SA, Hartig SM, McKenna NJ, Cox AR.   +4 more
europepmc   +1 more source

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The hypergeometric function, the confluent hypergeometric function and WKB solutions

Journal of the Mathematical Society of Japan, 2021
Relations between the hypergeometric function with a large parameter and Borel sums of WKB solutions of the hypergeometric differential equation with the large parameter are established. The confluent hypergeometric function is also investigated from the viewpoint of exact WKB analysis. As applications, asymptotic expansion formulas for those classical
Takashi Aoki, Mika Tanda, Toshinori Takahashi   +2 more
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The hypergeometric function

1966
The function represented by the infinite series \(\sum\limits_{n = 0}^\infty {\frac{{{{(a)}_n}{{(b)}_n}}}{{{{(c)}_n}}}\frac{{{z^n}}}{{n!}}} \) within its circle of convergence and all the analytic continuations is called the hypergeometric function 2 F 1(a, b; c;z).*
Wilhelm Magnus, Fritz Oberhettinger, Raj Pal Soni   +2 more
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Extended hypergeometric and confluent hypergeometric functions

Applied Mathematics and Computation, 2004
An extension of the beta function by introducing an extra parameter, which proved to be useful earlier, is applied here to extend the hypergeometric and confluent hypergeometric functions. Since the latter functions contain many of the familiar special functions as sub-cases, this extension is expected to prove to be useful.
M. Aslam Chaudhry, Asghar Qadir, Richard B. Paris, Hari M. Srivastava   +3 more
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The Hypergeometric Function

1998
Abstract Because of the many relations connecting the special functions to each other, and to the elementary functions, it is natural to inquire whether more general functions can be developed so that the special functions and elementary functions are merely specializations of these general functions.
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PATH HYPERGEOMETRIC FUNCTIONS

Journal of Algebra and Its Applications, 2007
Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the solutions of the Calogero–Sutherland model. If n = 2, the master function of the trace function is exactly the classical Gauss hypergeometric function.
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Multivariable Hypergeometric Functions

2001
The goal of this lecture is to present an overview of the modern developments around the theme of multivariable hypergeometric functions. The classical Gauss hypergeometric function shows up in the context of differential geometry, algebraic geometry, representation theory and mathematical physics.
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The Hypergeometric Functions

1999
Almost all of the elementary functions of mathematics are either hypergeometric or ratios of hypergeometric functions. A series Σ c n is hypergeometric if the ratio c n +1 / c n is a rational function of n . Many of the nonelementary functions that arise in mathematics and physics also have representations as hypergeometric series.
Ranjan Roy, Richard Askey, George E. Andrews   +2 more
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