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A transcriptomic microglia taxonomy across mouse and human pathologies. [PDF]

Nat Immunol
Chhatbar C, Sankowski R, Schulz M, Shimizu T, Schwabenland M, Staszewski O, Scheiwe C, Nessler S, Borst K, Dumas AA, Trost E, Berchtold D, Brandão W, Mossad O, Dalmau Gasull A, Frosch M, Erny D, Diebold M, Guffart E, Ternka K, Guranda M, Vinnakota JM, Friesen M, Ouk K, Waltl I, LaMorte M, Hammond TR, Di Liberto G, Vincenti I, Kreutzfeldt M, Mughrabi IT, Al-Abed Y, Blank T, Meyer-Luehmann M, Crow YJ, Hagen N, Ofengeim D, Zeiser R, Kettwig M, Gärtner J, Meisel A, Schwemmle M, Kalinke U, Beck J, Bengsch B, Thimme R, Butovsky O, Seredenina T, Ransohoff RM, Quintana FJ, Kierdorf K, Merkler D, Stadelmann C, Priller J, Prinz M.   +54 more
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Extended hypergeometric and confluent hypergeometric functions

Applied Mathematics and Computation, 2004
The functions under consideration are the extended Gaussian hypergeometric function \[ F_p(a,b;c,z)= {1\over B(b,c- b)} \int^1_0 t^{b-1}(1- t)^{c-b-1}(1- zt)^{-a}\exp\Biggl[-{p\over t(1- t)}\Biggr]\,dt \] and its confluent counterpart \(\Phi_p(b;c;z)\) with \(\exp(zt)\) in place of \((1- zt)^{-a}\). The authors discuss differentiation with respect to \(
Asghar Qadir, R B Paris
exaly   +3 more sources

Operator Hypergeometric Functions

Journal of Mathematical Sciences, 2023
The paper deals with differential equations \[ Du=Au\tag{1} \] with a differential operator \(D\) and unbounded operator coefficients \(A\). If the case when the Cauchy problem for equation (1) is uniformly well-posed then its solution can be represented via transformation operator.
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ON q-HYPERGEOMETRIC FUNCTIONS

Far East Journal of Mathematical Sciences (FJMS), 2017
Summary: In this article, we study some results on meromorphic functions defined by \(q\)-hypergeometric functions. In addition, certain sufficient conditions for these meromorphic functions to satisfy a subordination property are also pointed out. In fact, these results extend known results of starlikeness, convexity, and close to convexity.
Challab, K. A., Darus, M., Ghanim, F.
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The hypergeometric function, the confluent hypergeometric function and WKB solutions

Journal of the Mathematical Society of Japan, 2021
Take the Gauss hypergeometric equation and instead of parameters \(a,b,c\) let us write \(a=\alpha_0+\alpha \eta, b=\beta_0+\beta\eta, c=\gamma_0+\gamma\eta\) and instead of the unknown function \(w\) let us take \(w=x^{-c/2}(1-x)^{(-1/2)(a+b-c+1)}\psi\). Then the equation is written in the form \[ (-\frac{d^2}{dx^2}+\eta^2Q)\psi=0,\quad Q=\sum_{j=0}^N
Aoki, Takashi, Takahashi, Toshinori, Tanda, Mika   +2 more
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A Hypergeometric Function Transform

Journal of the Society for Industrial and Applied Mathematics, 1964
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Recurrences for hypergeometric functions

2003
Summary: Many of the known recurrences for the hypergeometric functions of several variables involve more than two parameters. A method is developed which allows a search of the functions for recurrences which involve only a specific number of the parameters, in particular, two parameter recurrences.
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Hypergeometric function representations

Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96, 1996
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HYPERgeometric functions DIfferential REduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: FD and FS Horn-type hypergeometric functions of three variables

Computer Physics Communications, 2014
Sven-Olaf Moch, Mikhail Kalmykov
exaly  

The generalized hypergeometric function

ACM SIGPLAN Notices, 1970
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