In this paper, some new integrals involving k gamma function and k digamma function have been established. An integral is established involving k gamma function, and its special values are discussed. Similarly, some new integrals have been established for k digamma function, and different elementary function is associated with it for different values of k. A nice representation of the Euler-Mascheroni constant and π in the form of k digamma function for different values of k is also obtained.

中文翻译：

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一些涉及 k gamma 和 k digamma 函数的积分

本文建立了一些涉及k gamma函数和k digamma函数的新积分。建立了一个涉及k个伽马函数的积分，并讨论了它的特殊值。类似地，已经为 k digamma 函数建立了一些新的积分，并且对于不同的 k 值，不同的初等函数与它相关联。对于不同的 k 值，还以 k digamma 函数的形式很好地表示了 Euler-Mascheroni 常数和 π。