Seán M. Stewart recently joined Nazarbayev University in Astana where he is an associate professor of engineering mathematics. Before moving to Kazakhstan, he spent eleven years working at The Petroleum Institute in Abu Dhabi, United Arab Emirates, where he was an associate professor in the Department of Mathematics. His main research interests lie in the fields of applied mathematics and in the history of computation.R. Barry Johnson has been involved for over 40 years in infrared technology, lens design, optical systems design, and electro-optical systems engineering, and has used many of the devices and techniques described in this book, and knew many of the individuals mentioned therein. He developed the method of integrating Planck’s equation using the method of Gauss–Laguerre quadrature. Dr Johnson is a Senior Research Professor at Alabama A&M University and has been a faculty member at two other academic institutions engaged in optics education and research, employed by a number of companies, and has provided consulting services within the field. Dr. Johnson is an SPIE Fellow and Life Member, OSA Fellow, and is an SPIE past president (1987). He has been awarded many patents and has published numerous scientific and technical articles. Dr. Johnson was awarded the 2012 OSA/SPIE Joseph W. Goodman Book Writing Award for Lens Design Fundamentals, Second Edition. He is a perennial co-chair of the annual SPIE Conference Current Developments in Lens Design and Optical Engineering.

"This is an excellent history of the mathematical development behind radiation calculators and other computational aids told in terms of detailed mathematical analysis and historical narrative. It is well-written, comprehensive, and includes the most extensive treatment of the radiation slide rule I have seen anywhere." — Barbara G. Grant, Author of Field Guide to Radiometry, Getting Started with UAV Imaging Systems: A Radiometric Guide and co-author of The Art of Radiometry, Cupertino, California, USA"The historical and mathematical details presented cannot be found in other books. It is a historic document, an impressive milestone. This book is not only very valuable for someone who wishes to understand the behavior of a blackbody, I recommend it also to those who are familiar with the subject, but want to know it all."—Max J. Riedl, Author and Lecturer, Germany"Blackbody radiation is covered in a wide and comprehensive sense, covering historical context, mathematical details, computational means and applications. This is easily the most comprehensive and well-researched compilation on blackbody radiation ever written. The book broadly follows a historical timeline, showing how the best available technology available at the time was used to compute results from Planck’s law. The book captures the ingenious beauty of mathematics, the nomogram and the slide rule to compute one of the most important physics laws in engineering."—CJ (Nelis) Willers, Airbus Optronics South Africa

• SECTION I: THE BLACKBODY PROBLEMChapter 1. Thermal radiation and the blackbody problem1.1 Towards a solution to the blackbody problem1.2 Planck and the blackbody problem1.3 The work of the experimentalists1.4 Thermal laws from dimensional analysis1.5 Transition and new beginningsSECTION II: THEORETICAL AND NUMERICAL MATTERSChapter 2. Theoretical developments2.1 Spectral representations2.2 Two important special functions2.2.1 Polylogarithms2.2.2 The Lambert W function2.3 Two common spectral scales used to represent blackbody radiation2.4 Other spectral scale representations2.5 Ephemeral spectral peaks2.6 Logarithmic spectral scales2.7 The radiometric and actinometric cases2.8 Normalized spectral exitance2.9 The Stefan–Boltzmann law2.9.1 The traditional approach2.9.2 A polylogarithmic approach2.10 Fractional functions of the ?rst kind2.11 Fractional functions of other kinds2.12 Centroid and median wavelengths2.13 The standard probability distribution and cumulative probability distribution functions for blackbody radiation2.14 Infrared, visible, and ultraviolet components in the spectral distribution of blackbody radiationChapter 3. Computational and numerical developments3.1 Approximations to the spectral exitance3.1.1 The laws of Wien and Rayleigh–Jeans3.1.2 Extended Wien and Rayleigh–Jeans approximations3.1.3 Polynomial interpolation and logarithmic correction factors3.1.4 Laurent polynomials and non-rational approximations of Erminy3.2 Computation of the fractional function of the ?rst kind3.2.1 Series expansion methods3.2.1.1 Large arguments3.2.1.2 Small arguments3.2.1.3 Division point<

Seán M. Stewart recently joined Nazarbayev University in Astana where he is an associate professor of engineering mathematics. Before moving to Kazakhstan, he spent eleven years working at The Petroleum Institute in Abu Dhabi, United Arab Emirates, where he was an associate professor in the Department of Mathematics. His main research interests lie in the fields of applied mathematics and in the history of computation.R. Barry Johnson has been involved for over 40 years in infrared technology, lens design, optical systems design, and electro-optical systems engineering, and has used many of the devices and techniques described in this book, and knew many of the individuals mentioned therein. He developed the method of integrating Planck’s equation using the method of Gauss–Laguerre quadrature. Dr Johnson is a Senior Research Professor at Alabama A&M University and has been a faculty member at two other academic institutions engaged in optics education and research, employed by a number of companies, and has provided consulting services within the field. Dr. Johnson is an SPIE Fellow and Life Member, OSA Fellow, and is an SPIE past president (1987). He has been awarded many patents and has published numerous scientific and technical articles. Dr. Johnson was awarded the 2012 OSA/SPIE Joseph W. Goodman Book Writing Award for Lens Design Fundamentals, Second Edition. He is a perennial co-chair of the annual SPIE Conference Current Developments in Lens Design and Optical Engineering.

"This is an excellent history of the mathematical development behind radiation calculators and other computational aids told in terms of detailed mathematical analysis and historical narrative. It is well-written, comprehensive, and includes the most extensive treatment of the radiation slide rule I have seen anywhere." — Barbara G. Grant, Author of Field Guide to Radiometry, Getting Started with UAV Imaging Systems: A Radiometric Guide and co-author of The Art of Radiometry, Cupertino, California, USA"The historical and mathematical details presented cannot be found in other books. It is a historic document, an impressive milestone. This book is not only very valuable for someone who wishes to understand the behavior of a blackbody, I recommend it also to those who are familiar with the subject, but want to know it all."—Max J. Riedl, Author and Lecturer, Germany"Blackbody radiation is covered in a wide and comprehensive sense, covering historical context, mathematical details, computational means and applications. This is easily the most comprehensive and well-researched compilation on blackbody radiation ever written. The book broadly follows a historical timeline, showing how the best available technology available at the time was used to compute results from Planck’s law. The book captures the ingenious beauty of mathematics, the nomogram and the slide rule to compute one of the most important physics laws in engineering."—CJ (Nelis) Willers, Airbus Optronics South Africa

• SECTION I: THE BLACKBODY PROBLEMChapter 1. Thermal radiation and the blackbody problem1.1 Towards a solution to the blackbody problem1.2 Planck and the blackbody problem1.3 The work of the experimentalists1.4 Thermal laws from dimensional analysis1.5 Transition and new beginningsSECTION II: THEORETICAL AND NUMERICAL MATTERSChapter 2. Theoretical developments2.1 Spectral representations2.2 Two important special functions2.2.1 Polylogarithms2.2.2 The Lambert W function2.3 Two common spectral scales used to represent blackbody radiation2.4 Other spectral scale representations2.5 Ephemeral spectral peaks2.6 Logarithmic spectral scales2.7 The radiometric and actinometric cases2.8 Normalized spectral exitance2.9 The Stefan–Boltzmann law2.9.1 The traditional approach2.9.2 A polylogarithmic approach2.10 Fractional functions of the ?rst kind2.11 Fractional functions of other kinds2.12 Centroid and median wavelengths2.13 The standard probability distribution and cumulative probability distribution functions for blackbody radiation2.14 Infrared, visible, and ultraviolet components in the spectral distribution of blackbody radiationChapter 3. Computational and numerical developments3.1 Approximations to the spectral exitance3.1.1 The laws of Wien and Rayleigh–Jeans3.1.2 Extended Wien and Rayleigh–Jeans approximations3.1.3 Polynomial interpolation and logarithmic correction factors3.1.4 Laurent polynomials and non-rational approximations of Erminy3.2 Computation of the fractional function of the ?rst kind3.2.1 Series expansion methods3.2.1.1 Large arguments3.2.1.2 Small arguments3.2.1.3 Division point<