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Explore the remarkable properties and widespread applications of the Källén function in this mathematical lecture. Discover how this elementary yet ubiquitous function, while less well-known than the exponential function, connects diverse areas of mathematics and physics. Learn about its origins in elementary mathematics and its subsequent rediscovery by physicists for scattering amplitude calculations. Examine the function's connections to combinatorial generating functions for Catalan numbers, solutions of classical ordinary differential equations of Bessel-type, and generalized hypergeometric functions of Appell and Kampé de Férie. Investigate its relationships to the Wigner-Bloch dilogarithm, properties of discriminants, and associativity of 2-valued multiplication laws. Gain insights into the interconnected nature of mathematical concepts through engaging stories and examples that illustrate the Källén function's significance across multiple mathematical domains.
