Complements of Higher Mathematics pp 53-87 | Cite as

Special Functions

• Authors
• Authors and affiliations

• Marin Marin
• Andreas Öchsner

Chapter

First Online: 14 February 2018

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Abstract

Consider the semi-plane \(\Delta _0=\{z\in C,\;z=x+iy:x>0\}\). The complex function \(\Gamma :\Delta _0\rightarrow C\) defined by

$$ \Gamma (z)=\int \limits _{0}^{\infty }t^{z-1}e^{-t}\mathrm {d}t, $$

is called the Euler’s function of first species.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

• Marin Marin
  • 1
  Email author
• Andreas Öchsner
  • 2

1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingen am NeckarGermany