polygamma
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1: 5.15 Polygamma Functions
§5.15 Polygamma Functions
►The functions , , are called the polygamma functions. In particular, is the trigamma function; , , are the tetra-, penta-, and hexagamma functions respectively. … ►
5.15.2
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►For see §24.2(i).
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2: 5.24 Software
3: 5.21 Methods of Computation
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►For the left half-plane we can continue the backward recurrence or make use of the reflection formula (5.5.3).
►Similarly for , , and the polygamma functions.
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4: 5.16 Sums
§5.16 Sums
…5: 5.22 Tables
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§5.22(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 6) tabulates , , , and for to 10D; and for to 10D; , , , , , , , and for to 8–11S; for to 20S. …6: Software Index
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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5.24(iii) , , | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||
5.24(iv) , , , | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||||
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7: Bibliography
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Polygamma functions of negative order.
J. Comput. Appl. Math. 100 (2), pp. 191–199.
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8: Bibliography K
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Calculation of complex polygamma functions.
Sci. Rep. Hirosaki Univ. 43 (1), pp. 161–183.
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9: Bibliography B
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Computation of the polygamma functions.
Comm. Statist. B—Simulation Comput. 13 (3), pp. 409–415.
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