单词 | Polygamma Function | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
释义 | Polygamma FunctionThe polygamma function is sometimes denoted
where ![]() ![]() ![]()
where ![]() ![]() ![]() ![]()
![]() ![]() ![]() ![]() The polygamma function obeys the Recurrence Relation
![]() In general, special values for integral indices are given by
giving
and so on. R. Manzoni has shown that the polygamma function can be expressed in terms of Clausen Functions for Rational arguments and integer index. Special cases are given by
See also Clausen Function, Digamma Function, Gamma Function, Stirling's Series
Abramowitz, M. and Stegun, C. A. (Eds.). ``Polygamma Functions.'' §6.4 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 260, 1972. Adamchik, V. S. ``Polygamma Functions of Negative Order.'' Submitted to J. Symb. Comput. Arfken, G. ``Digamma and Polygamma Functions.'' §10.2 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 549-555, 1985. Davis, H. T. Tables of the Higher Mathematical Functions. Bloomington, IN: Principia Press, 1933. Kolbig, V. ``The Polygamma Function Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 422-424, 1953. |
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