SECTION I: THE BLACKBODY PROBLEM

Chapter
1. Thermal radiation and the blackbody problem



1.1 Towards a solution to the blackbody problem



1.2 Planck and the blackbody problem



1.3 The work of the experimentalists



1.4 Thermal laws from dimensional analysis



1.5 Transition and new beginnings



SECTION II: THEORETICAL AND NUMERICAL MATTERS



Chapter
2. Theoretical developments



2.1 Spectral representations



2.2 Two important special functions



2.2.1 Polylogarithms



2.2.2 The Lambert W function



2.3 Two common spectral scales used to represent blackbody radiation



2.4 Other spectral scale representations



2.5 Ephemeral spectral peaks



2.6 Logarithmic spectral scales



2.7 The radiometric and actinometric cases



2.8 Normalized spectral exitance



2.9 The Stefan?Boltzmann law



2.9.1 The traditional approach



2.9.2 A polylogarithmic approach



2.10 Fractional functions of the ?rst kind



2.11 Fractional functions of other kinds



2.12 Centroid and median wavelengths



2.13 The standard probability distribution and cumulative probability distribution functions for blackbody radiation



2.14 Infrared, visible, and ultraviolet components in the spectral distribution of blackbody radiation



Chapter
3. Computational and numerical developments



3.1 Approximations to the spectral exitance



3.1.1 The laws of Wien and Rayleigh?Jeans



3.1.2 Extended Wien and Rayleigh?Jeans approximations



3.1.3 Polynomial interpolation and logarithmic correction factors



3.1.4 Laurent polynomials and non-rational approximations of Erminy



3.2 Computation of the fractional function of the ?rst kind



3.2.1 Series expansion methods



3.2.1.1 Large arguments



3.2.1.2 Small arguments



3.2.1.3 Division point