E710 -- Specimen transformationis singularis serierum

(Example of the transformation of singular series)

Summary:

Euler starts with a hypergeometric series F(a, b, c, x), and differentiates it to get a functional relation. Then he integrates to get another and ends up with something like Legendre polynomials.

Publication:

Originally published in Nova Acta Academiae Scientarum Imperialis Petropolitinae 12, 1801, pp. 58-70
Opera Omnia: Series 1, Volume 16, pp. 41 - 55

Documents Available:

The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E710 include:
- Mostow GD., “Braids, hypergeometric-functions, and lattices.” Bulletin of the American Mathematical Society, 16 (2), pp. 225-246 (Apr 1987).

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