Charles A Nelson and Michael G Gartley 1996 J. Phys. A: Math. Gen. 29 8099 doi:10.1088/0305-4470/29/24/031
On the two q-analogue logarithmic functions: 
Charles A Nelson and Michael G Gartley
Show affiliationsThere is a simple, multi-sheet Riemann surface associated with 
's inverse function 
for 
. A principal sheet for can be defined. However, the topology of the Riemann surface for changes each time q increases above the collision point 
of a pair of the turning points 
of 
. There is also a power series representation for 
. An infinite-product representation for is used to obtain the ordinary natural logarithm 
and the values of the sum rules 
for the zeros 
of . For 
, 
where 
. The values of the sum rules for the q-trigonometric functions, 
and 
, are q-deformations of the usual Bernoulli numbers.
- PACS
- MSC
- Subjects
- Dates
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Issue 24 (21 December 1996)
Received 19 August 1996
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On the two q-analogue logarithmic functions:
Charles A Nelson and Michael G Gartley 1996 J. Phys. A: Math. Gen. 29 8099
-
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