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βΊ
denotes the number of compositions of , and is the number of compositions into exactlyparts.
is the number of compositions of with no 1’s, where again .
The integer 0 is considered to have one composition consisting of no parts:
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βΊ
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βΊAbramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients for up to 50 and up to 25; extends Table 26.4.1 to ; tabulates Stirling numbers of the first and second kinds, and , for up to 25 and up to ; tabulates partitions and partitions into distinct parts
for up to 500.
βΊAndrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts
, partitions into parts
, and unrestricted plane partitions up to 100.
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βΊFigure 19.3.9:
as a function of complex for , .
The real part is symmetric under reflection in the real axis.
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Magnify3DHelpβΊβΊ
βΊFigure 19.3.10:
as a function of complex for , .
The imaginary part is 0 for , and is antisymmetric under reflection in the real axis.
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Magnify3DHelpβΊβΊ
βΊFigure 19.3.11:
as a function of complex for , .
The real part is symmetric under reflection in the real axis.
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Magnify3DHelpβΊβΊ
βΊFigure 19.3.12:
as a function of complex for , .
The imaginary part is 0 for and is antisymmetric under reflection in the real axis.
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Magnify3DHelp