• Corpus ID: 237572260

Hyperelliptic values of the Gamma function

@inproceedings{Lugering2021HyperellipticVO,
  title={Hyperelliptic values of the Gamma function},
  author={Jan Lugering},
  year={2021}
}

• Jan Lugering
• Published 19 September 2021
• Mathematics

We determine new particular values of the Gamma function for specific rational arguments in the interval (0,1). Introducing hyperelliptic generalisations of the trigonometric functions, we obtain a halving formula for specific rational arguments. Then we define a family of functions, which encompasses the exponential function. We present an overlooked integral definition by Gauß and explore a few general formulas for the Gamma function. Finally, we apply the new values of the Gamma function to compute certain singular values of the complete elliptic integral and some arithmetic-geometric-means and give the area of certain superellipses.