A UNIFIED APPROACH TO THE PAINLEVE TRANSCENDENTS

作者：Steinmetz Norbert^*

来源：Annales Academiae Scientiarum Fennicae-Mathematica, 2017, 42(1): 17-49.

DOI：10.5186/ansfm.2017.4203

• Stokes sector
• Stokes ray
• asymptotic expansion
• re-scaling
• pole-free sector
• Airy equation
• Weber-Hermite equation
• sub-normal solution

We utilise a recent approach via the so-called re-scaling method to derive a unified and comprehensive theory of the solutions to Painleve's differential equations (I), (II) and (IV), with emphasis on the most elaborate equation (IV).

• 出版日期2017