论文信息 - The Planck integral cannot be evaluated in terms of a finite series of elementary functions

The Planck integral cannot be evaluated in terms of a finite series of elementary functions

It is shown that the Planck integral cannot be evaluated in terms of a finite series of elementary functions. A relation is first established between the Planck and dilogarithm integrals. To prove nonintegrability the Risch decision procedure for elementary functions is then applied to the dilogarithm integral.

Richard Pavelle

[1] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[2] R. Risch. The problem of integration in finite terms , 1969 .

[3] R. Barry Johnson,et al. Integration of Planck's equation by the Laguerre-Gauss quadrature method. , 1974 .

[4] D. Wilcox,et al. A method for the resolution of multiple graybodies from spectrally sampled optical systems , 1979 .