psi function
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11—20 of 102 matching pages
11: 5.10 Continued Fractions
§5.10 Continued Fractions
…12: 5.19 Mathematical Applications
13: 5.15 Polygamma Functions
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►The functions
, , are called the polygamma functions.
In particular, is the trigamma function; , , are the tetra-, penta-, and hexagamma functions respectively.
Most properties of these functions follow straightforwardly by differentiation of properties of the psi function.
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5.15.1
,
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5.15.5
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14: 25.16 Mathematical Applications
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►In studying the distribution of primes , Chebyshev (1851) introduced a function
(not to be confused with the digamma function used elsewhere in this chapter), given by
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25.16.1
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25.16.2
,
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25.16.3
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25.16.4
,
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15: 5.6 Inequalities
16: 36.6 Scaling Relations
17: 36.3 Visualizations of Canonical Integrals
18: 36.2 Catastrophes and Canonical Integrals
19: 17.1 Special Notation
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►The main functions treated in this chapter are the basic hypergeometric (or -hypergeometric) function
, the bilateral basic hypergeometric (or bilateral -hypergeometric) function
, and the -analogs of the Appell functions
, , , and .
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