Ln-变换、L2n-transform和P2n变换的恒等式及其应用

欧几里得空间中与声纳变换和Radon变换有关的算子恒等式

Operator identities relating sonar and Radon transforms in Euclidean space

我们建立了新的关系，连接欧几里德声纳变换（在超平面中的中心的领域采取的积分）与经典的Radon变换。的关系，表示为运营商的身份，使我们能够减少到经典的氡反演声纳变换的反演。

Extensions of the Classical Transformations of 3F2

It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple's ident…

Several classical identities via Mellin's transform

We present a summation rule using the Mellin transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative integers are expressed in terms of Bernoulli polynomials. We also show identities involving exponential and Hermite polynomials.

Bernoulli数、欧拉数和Riemann zeta值的某些恒等式、联系和显式

Certain identities, connection and explicit formulas for the Bernoulli, Euler numbers and Riemann zeta -values

建立了Bernoulli数、欧拉数和Riemann zeta函数值的各种新的恒等式、递推关系、整表示、联系和显式。要做到这一点，我们探讨一些谢弗的多项式序列相关的Kontorovich-Lebedev变换的属性。

Hilbert变换的Rellich恒等式

Rellich identities for the Hilbert transform

本文利用Rellich恒等式和图Lipschitz区域上的Neumann问题证明涉及共形映射的Hilbert变换恒等式，并由此得到新的加权L^2估计及与Helson-Szegö定理相关的精确范数界。

Integrals and Series Representations of $q$-Polynomials and Functions: Part II Schur Polynomials and the Rogers-Ramanujan Identities

We give several expansion and identities involving the Ramanujan function $A_q$ and the Stieltjes--Wigert polynomials. Special values of our idenitities give $m$-versions of some of the items on the Slater list of Rogers-Ramanujan type identities. We also study some bilateral extensions of certain transformations in the theory of basic hypergeometric functions.

用第二类Stirling数计算欧拉多项式的显式公式

Explicit formulae for computing Euler polynomials in terms of Stirling numbers of the second kind

本文初步统一和推广了涉及函数$\frac{\pm1}{e^{\pm t}-1}$及其导数的八个恒等式。利用其中的一个恒等式，作者建立了计算欧拉多项式和双参数欧拉多项式的两个显式公式。

Bailey型变换及其应用

Bailey Type Transforms and Applications

本文的目的是建立新的Bailey型级数变换，并证明这些Bailey型变换与经典的Bailey型变换一样有效，不仅给出新的$q$ -超几何恒等式，- 将二重或三重级数转换成非常平稳的$_{10}Φ_9$或$_{12}Φ_{11}$级数，但也可用于导出新的二重和三重级数Rogers-Ramanujan型恒等式和相应的Rogers-Ramanujan型恒等式的无限族。

涉及指数函数、导数和第二类Stirling数的八个有趣恒等式

Eight interesting identities involving the exponential function, derivatives, and Stirling numbers of the second kind

本文建立了函数$\frac1{(1-e^{\pm t})^k}$及其导数$\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}$可以用第二类组合数和Stirling数的系数线性组合表示的恒等式，其中$t\ne0$和$i,k\in\mathbb{N}$ .

Koshliakov核与包含黎曼ζ函数的恒等式

Koshliakov kernel and identities involving the Riemann zeta function

研究了涉及黎曼ζ函数和函数倒数在Bessel函数$J_{z}(x), Y_{z}(x)$和$K_{z}(x)$核中的积分恒等式.有趣的特殊情况下，这些身份的推导，其中之一是连接到一个众所周知的转换由于拉马努金，和Guinand。

Painlevé第三次超越的新转变

New Transformations for Painlevé's Third Transcendent

我们提出的转换有关的第三个超越的Painlevé与参数集位于角落的Weyl室的对称群的系统，仿射外尔群的根系$ B^{(1)}_2 $，那些在原点。这种变换需要一个自变量的缩放，并意味着添加剂的身份为规范的哈密顿和产品的身份为$τ$ -功能与这些参数集。