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It is well-known that the Bhattacharyya, Hellinger, Kullback-Leibler, $\alpha$-divergences, and Jeffreys' divergences between densities belonging to a same exponential family have generic closed-form formulas relying on the strictly convex and real-analytic cumulant function characterizing the exponential family.
Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen
Constantin Carathéodory · 1907
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Neue begründung der theorie quadratischer formen von unendlichvielen veränderlichen
Ernst Hellinger · 1909
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The generalised product moment distribution in samples from a normal multivariate population
John Wishart · 1928
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On a measure of divergence between two multinomial populations
Anil Bhattacharyya · 1946
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An invariant form for the prior probability in estimation problems
Harold Jeffreys · 1946
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A mathematical theory of communication
Claude E Shannon · 1948
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On information and sufficiency
Solomon Kullback and Richard A Leibler · 1951
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A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations
Herman Chernoff et al · 1952
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The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
Lev M. Bregman · 1967
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Information-type measures of difference of probability distributions and indirect observation
Imre Csiszár · 1967
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The divergence and Bhattacharyya distance measures in signal selection
Thomas Kailath · 1967
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The solution of the problem of integration in finite terms
Robert H Risch · 1970
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Francis Clarke · 1976
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Teofilo F Gonzalez · 1985
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Joan Del Castillo · 1994
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Patrick Billingsley · 1995
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