Lerch transcendent
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1: 25.14 Lerch’s Transcendent
§25.14 Lerch’s Transcendent
►§25.14(i) Definition
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25.14.1
; .
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►The Hurwitz zeta function (§25.11) and the polylogarithm (§25.12(ii)) are special cases:
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§25.14(ii) Properties
…2: 25.1 Special Notation
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►The main related functions are the Hurwitz zeta function , the dilogarithm , the polylogarithm (also known as Jonquière’s function ), Lerch’s transcendent
, and the Dirichlet -functions .
3: 25.21 Software
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§25.21(viii) Lerch’s Transcendent
…4: Software Index
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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25.21(viii) Lerch’s Transcendent | a | ✓ | ✓ | ✓ | a | ||||||||||||||||||||
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5: Bibliography
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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6: Errata
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Equation (25.14.1)
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the previous constraint was removed. A clarification regarding the correct constraints for Lerch’s transcendent has been added in the text immediately below. In particular, it is now stated that if is not an integer then ; if is a positive integer then ; if is a non-positive integer then can be any complex number.