By Bruce C. Berndt, Ken Ono (ed.)

The topic of $q$-series may be stated firstly Euler and his pentagonal quantity theorem. in truth, $q$-series are often known as Eulerian sequence. Contributions have been made by way of Gauss, Jacobi, and Cauchy, however the first try out at a scientific improvement, particularly from the viewpoint of learning sequence with the goods within the summands, used to be made by way of E. Heine in 1847. within the latter a part of the 19th and within the early a part of the 20th centuries, English mathematicians, L. J. Rogers and F. H. Jackson, made basic contributions.In 1940, G. H. Hardy defined what we now name Ramanujan's recognized $_1\psi_1$ summation theorem as 'a outstanding formulation with many parameters'. this can be now one of many basic theorems of the topic. regardless of humble beginnings, the topic of $q$-series has flourished long ago 3 a long time, really with its functions to combinatorics, quantity idea, and physics. throughout the yr 2000, the college of Illinois embraced The Millennial yr in quantity idea. one of many occasions that 12 months was once the convention $q$-Series with purposes to Combinatorics, quantity conception, and Physics. This occasion collected mathematicians from across the world to lecture and speak about their learn. This quantity offers nineteen of the papers awarded on the convention. the wonderful lectures which are integrated chart pathways into the longer term and survey the varied functions of $q$-series to combinatorics, quantity idea, and physics

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**Extra resources for Q-Series With Applications to Combinatorics, Number Theory, and Physics: A Conference on Q-Series With Applications to Combinatorics, Number Theory, ... of Illinois**

**Sample text**

Here the doped layers are very thin compared to the complete thickness of the diode. The j13 j 1 Introduction to Thin-Film Photovoltaics 14 largest share of the complete absorber thickness is occupied by an intrinsic, that is, undoped layer, in between the n and p-type regions. 5 V. Under short-circuit conditions, the region with a nonzero electric ﬁeld extends over the complete intrinsic layer. Only directly at the contacts, the ﬁeld is relatively small. 6d. Solar cells made from a-Si:H as well as a-Si:H/mc-SiH tandem cells use the p–i–n conﬁguration.

The superstrate is followed by layers which are part of the front contact, followed by the absorber layer and the layers that form the back contact. The second possibility is to inverse the layer stack, starting with the front contact, the absorber, and the back contact. These layers are all deposited on top of a substrate that is now not at the illuminated side of the device. Thus, the substrate can be transparent or opaque. 10 Sketch of the layer sequences to build up the system for thin-film solar cells in (a) superstrate and (b) substrate configuration.

Cu(In,Ga)Se2 and CdTe solar cells are examples for p–n-(hetero)junctions. For some disordered semiconductors like amorphous silicon, the electronic quality of doped layers is very poor. In addition, the mobilities and diffusion lengths are small, and thus purely diffusive transport would not lead to efﬁcient charge extraction. The solution to this problem is the so-called p–i–n-junction diode. Here the doped layers are very thin compared to the complete thickness of the diode. The j13 j 1 Introduction to Thin-Film Photovoltaics 14 largest share of the complete absorber thickness is occupied by an intrinsic, that is, undoped layer, in between the n and p-type regions.