7,473 research outputs found
Identical relations on some special polynomials
No full text碩士我們主要是延續Kung-Yu Chen 和H.M. Srivastava兩位教授的一些研究。利用生成函數以及複變數的一些理論繼而得到一些關於超幾何多項式的恒等式。特別地，我們得到更多的有關古典的Laguerre 多項式之一些恆等式。相較於Bavinck使用微分算子的技巧得到Laguerre 多項式關係式，我們引進了更簡單的方法。The main object of this paper is to a continatire work of Kung-Yu Chen and H.M. Srivastava. We use generating functions and a few theory of complex variables to obtain some new results for Hypergeometric Polynomials.Particularly, we obtain more identities about classic Laguerre pynomial. Compare with the relationship about Laguerre pynomials made by Bavink who use of the differential operator to prove, we find a method more simple then him.目錄
Intruduction……………………………………………………p.1
第一章 超幾何多項式Hypergeometric polynomials
1.1 定義與基本性質…………………………………………………..p.2
1.2 超幾何函數之恆等式……………………………………………..p.8
1.3 Remark……………………………………………………………..p.19
第二章 Srivastava-Singhal polynomials
2.1 定義與基本性質…………………………………………………..p.22
2.2 Srivastava-Singhal polynomials 之恆等式…………p.23
參考文獻...................................................p.34學號: 692150013, 學年度: 9
Telema liangxi Zhu & Chen 2002
No full textTelema liangxi Zhu & Chen, 2002 T. liangxi Zhu & Chen, 2002: 82, f. 1–7. (Male holotype, 2 female paratypes from China: Guizhou: Liangxi Cave, Dongtang Town [25 º 12 ʹN, 108 º00ʹE], Maolan National Natural Reserve, Libo County, 5 Nov. 1999, H.M. Chen leg., deposited in College of Life Sciences, Hubei University, Baoding, not examined) Material examined. None. Diagnosis. Telema liangxi seems closest to T. strentarsi, but the male of former may be distinguished by the blunt embolus distally and the distinctly pear-shaped bulb, the female by the long and coiled spermatheca that swollen proximally and distally, contracted mesially (Zhu & Chen, 2002, figs. 4–6). Description. See Zhu and Chen (2002). Distribution. China (Guizhou) (Fig. 20).Published as part of Lin, Yucheng & Li, Shuqiang, 2010, Long-legged cave spiders (Araneae, Telemidae) from Yunnan-Guizhou Plateau, southwestern China, pp. 1-34 in Zootaxa 2445 on page 15, DOI: 10.5281/zenodo.19503
sj-docx-1-jdr-10.1177_00220345211056247 – Supplemental material for Global Burden and Inequality of Dental Caries, 1990 to 2019
No full textSupplemental material, sj-docx-1-jdr-10.1177_00220345211056247 for Global Burden and Inequality of Dental Caries, 1990 to 2019 by P.Y.F. Wen, M.X. Chen, Y.J. Zhong, Q.Q. Dong and H.M. Wong in Journal of Dental Research</p
Glyphiulus liangshanensis Chen 2017, sp. nov.
No full textGlyphiulus liangshanensis sp. nov. Figs 7A‒F, 8A‒F, 9A‒B, 10A‒E Type material. Holotype male, China: Sichuan Province, Liangshan Yi Autonomous Prefecture, Xichang City, Xixi, Xianren Cave (27°42'36.90"N, 102°18'25.68"E), 29 October 2015, H.M. Chen leg. (IBGAS). Paratypes: 6 males, 3 females and 4 juveniles, same data as holotype; 1 male and 1 juvenile, Sichuan Province, Liangshan Yi Autonomous Prefecture, Miyi County, Baima Town, Zhuanxulong Cave (26°59'55.79"N, 102°12'23.97"E), 27 October 2015, H.M. Chen leg. (IBGAS). Etymology. This specific name is derived from the type locality. Diagnosis. The new species differ from other species in this genus except Glyphiulus intermedius Golovatch, Geoffroy, Mauriès & Van den Spiegel, 2007 (Golovatch et al. 2007b: 446, figs 25, 26) also from Sichuan Province by the special carinotaxic formula of the collum (I+2c+III‒IV+5c+6a+pc+ma+pc+6a+5c+IV‒III+2c+I). It can be differentiated from Glyphiulus intermedius by the elongated, slender and slightly laterad curved coxosternal mesal processes of the anterior gonopods, and the short lamelliform lobe of the coxite of the posterior gonopods. Description. Holotype with 55p + 1a + T, 37 mm long and 1.9 mm wide; paratypes (male, female) with 38‒62p + 1‒4a + T, length 16.5‒40 mm, width 1.3‒1.9 mm. Coloration light yellow-brown to red-brown (Figs 7A‒F). Clypeus with four teeth anteromedially (Fig. 10C). All characters as in Glyphiulus latus sp. nov., except as follows. Adults with 7‒13 blackish eyes in a nearly triangular patch on each side of the head (Fig. 7A). Collum strongly crested, carinotaxic formula (I+2c+III‒IV+5c+6a+pc+ma+pc+6a+5c+IV‒III+2c+I) (Figs 7A, B). Penes relatively small, each with 2 strong setae distolaterally (Figs 8C, 10E). The ratio of the length of midbody legs to body diameter is lower than Glyphiulus latus sp. nov.. Anterior gonopods with a pair of shield-like coxosterna, with a pair of elongated and slightly laterad curved mesal processes, which are longer than the 1-segmented telopodites (Figs 9A, 10A). Posterior gonopods brush-like paramedially; distally membranous, with long, curved and medially contiguous flagella (Figs 9B, 10B). Distribution. Known only from type locality, Sichuan, China. Notes. In the absence of any troglomorphic traits, this species can only be considered troglophilic at most.Published as part of Chen, Hui-Ming, 2017, Two new species of the millipede genus Glyphiulus Gervais, 1847 from Southwest China (Diplopoda: Spirostreptida: Cambalopsidae), pp. 197-208 in Zootaxa 4323 (2) on pages 203-204, DOI: 10.11646/zootaxa.4323.2.3, http://zenodo.org/record/89890
New representations for the Lugo and Euler–Mascheroni constants. II
No full textAbstractLugo’s constant L given by L=−12−γ+ln2 is defined as the limit of the sequence (Ln)n∈N defined by Ln:=∑i=1n∑j=1n1i+j−(2ln2)n+lnn(n∈N) as n→∞, N being the set of positive integers. In an earlier investigation [C.-P. Chen, H.M. Srivastava, New representations for the Lugo and Euler–Mascheroni constants, Appl. Math. Lett. 24 (2011) 1239–1244] we established new analytical representations for the Euler–Mascheroni constant γ in terms of the psi (or digamma) function ψ(z), gave the bounds for the difference L−Ln and presented a new sequence which was shown to converge to Lugo’s constant L. In this following article, we establish several further (presumably new) analytical representations for the Euler–Mascheroni constant γ in terms of the psi (or digamma) function ψ(z)
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