论文标题
复杂序列的一类转换的应用
Applications of a class of transformations of complex sequences
论文作者
论文摘要
通过针对2018年的Mishev引起的显着结果，该结果涉及一类复杂数字序列转换的倒置，我们为$ \ frac {1}π$ ramanujan获得了一个非常简单的证明。然后，我们应用Mishev的转换为许多相关的高几幅身份提供证明，包括莱夫里先前通过傅立叶 - legendre理论获得的$ \ frac {1}π$系列的新的和简化的证明。我们使用Mishev的变换概括了这一结果，以扩大涉及立方二项式系数和谐波数的Ramanujan样系列上的Guillera引起的结果。
Through an application of a remarkable result due to Mishev in 2018 concerning the inverses for a class of transformations of sequences of complex numbers, we obtain a very simple proof for a famous series for $\frac{1}π$ due to Ramanujan. We then apply Mishev's transform to provide proofs for a number of related hypergeometric identities, including a new and simplified proof for a family of series for $\frac{1}π$ previously obtained by Levrie via Fourier--Legendre theory. We generalize this result using Mishev's transform, so as to extend a result due to Guillera on a Ramanujan-like series involving cubed binomial coefficients and harmonic numbers.
