曹健

姓名：曹健

职称：教授

邮箱：21caojian@hznu.edu.cn

个人简介：江苏淮安人，华东师范大学博士，浙江大学博士后，法国里昂第一大学访问学者，教授，硕士生导师，从事组合数学与特殊函数领域的研究。主持国家青年基金、国家天元基金、中国博士后基金、浙江省青年及面上基金等项目，已在本领域(Stud. Appl. Math.、Adv. in Appl. Math.、Math. Nachr.等)重要学术刊物上以独立或通讯作者发表40余篇SCI论文，入选杭州市属高校中青年学术带头人、杭州市131人才，担任美国数学会评论员。多次在中国数学会学术年会、全国组合数学与图论、海峡两岸图论与组合数学、英国肯特大学及伦敦大学学院等国内外学术会议上作报告。

研究方向：组合数学与特殊函数

教学与课程：本科生《组合数学》、《高等数学》、《数学与人类文明》等

代表性论文（详见科研之友主页https://www.scholarmate.com/P/JianCAO）：

[1] J. Cao, The generalized q-heat equations for q-3D hypergeometric polynomials with applications to generating functions and Askey-Wilson integrals, Adv. in Appl. Math. 176(2026), Paper No. 103054, 32 pp.

[2] J. Cao, Homogeneous q-Laguerre type polynomials expansion for analytic functions via q-partial differential equations as well as generating functions and q-integrals, Period. Math. Hungar. 92(2026), no. 1, 103–124.

[3] J. Cao, Bivariate Rogers–Szegö polynomials expansions of q-operational equations with applications to Andrews–Askey integral and Ramanujan’s Master Theorem, J. Difference Equ. Appl. 2026, https://doi.org/10.1080/10236198.2026.2647969

[4] J. Cao, q-Partial differential equations for generalized q-2D ultraspherical polynomials with some applications, Front. Math. 2026, https://doi.org/10.1007/s11464-024-0068-7

[5] J. Cao and Y. Yang, Polynomial augmentation for Ramanujan's q-beta integral and related expansions of Ramanujan's Master Theorem, Ramanujan J. 2026, https://doi.org/10.1007/s11139-026-01404-7

[6] J. Cao, Y. Yang and S. Arjika, The homogeneous little q-Jacobi polynomials, Math. Nachr. 298(2025), no. 12, 3791–3815.

[7] B. He, L. Li and J. Cao, Some inequalities between M(a,b,c;L;n) and the partition function p(n), Canad. J. Math. 77(2025), no. 6, 2148–2170.

[8] J. Cao, Poisson kernels of q-3D Hermite polynomials expansion for functions of several variables via generalized q-heat equations, Trans. London Math. Soc. 12(2025), no. 1, Paper No. e70015, 30 pp.

[9] J. Cao, Q. Bao and S. Arjika, A note on expansions of q-exponential equations and q-Hardy–Hille type formulas, Bull. Sci. Math. 195(2024), Paper No. 103489, 24 pp.

[10] J. Cao, N. Raza and M. Fadel, Two-variable q-Laguerre polynomials from the context of quasi-monomiality, J. Math. Anal. Appl. 535(2024), no. 2, Paper No.128126, 24 pp..

[11] J. Cao, H.-L. Zhou and S. Arjika, Generalized q-difference equations for (q,c)-hypergeometric polynomials and some applications, Ramanujan J. 60 (2023), no. 4, 1033–1067.

[12] J. Cao, A note on q-difference equations for Ramanujan’s integrals, Ramanujan J. 48 (2019), no. 1, 63–73.

[13] J. Cao, H.M. Srivastava and Z.-G. Liu, Some iterated fractional q-integrals and their applications, Fract. Calc. Appl. Anal. 21 (2018), no. 3, 672–695.

[14] J. Cao and D.-W. Niu, q-Difference equations for Askey–Wilson type integrals via q-polynomials, J. Math. Anal. Appl. 452 (2017), no. 2, 830–845.

[15] J. Cao, Homogeneous q-partial difference equations and some applications, Adv. in Appl. Math. 84 (2017): 47–72.

[16] J. Cao and D.-W. Niu, A note on q-difference equations for Cigler's polynomials, J. Difference Equ. Appl. 22 (2016), no. 12, 1880–1892.

[17] J. Cao, Homogeneous q-difference equations and generating functions for q-hypergeometric polynomials, Ramanujan J. 40 (2016), no. 1, 177–192.

[18] J. Cao, q-difference equations for generalized homogeneous q-operators and certain generating functions, J. Difference Equ. Appl. 20(2014), no. 5-6, 837–851.

[19] J. Cao, A note on generalized q-difference equations for q-beta and Andrews-Askey integral, J. Math. Anal. Appl. 412(2014), no. 2, 841–851.

[20] J. Cao, A note on q-integrals and certain generating functions, Stud. Appl. Math. 131(2013), no. 2, 105–118.