THE MODULAR RELATION AND THE DIGAMMA FUNCTION

スポンサーリンク

概要

• 論文の詳細を見る

• In this paper we shall locate a class of fundamental identities for the gamma function and trigonometric functions in the chart of functional equations for the zeta-functions as a manifestation of the underlying modular relation. We use the beta-transform but not the inverse Heaviside integral. Instead we appeal to the reciprocal relation for the Euler digamma function which gives rise to the partial fraction expansion for the cotangent function. Through this we may incorporate basic results from the theory of the digamma (and gamma) function, thereby dispensing also with the beta-transform. Section 4 could serve as a foundation of the theory of the gamma function through the digamma function.

著者

• CHAKRABORTY K.

  Harish-Chandra Research Institute

• Kanemitsu Shigeru

  School of Humanity-Oriented Science and Engineering Kinki University

• Wang X.-H.

  Graduate School of Advanced Technology Kinki University

関連論文

• THE MODULAR RELATION AND THE DIGAMMA FUNCTION
• ARITHMETICAL FOURIER SERIES AND THE MODULAR RELATION

スポンサーリンク