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1: 26.9 Integer Partitions: Restricted Number and Part Size
See Table 26.9.1. …
26.9.2 p 0 ( n ) = 0 , n > 0 ,
26.9.8 p k ( n ) = p k ( n - k ) + p k - 1 ( n ) ;
2: 26.2 Basic Definitions
The total number of partitions of n is denoted by p ( n ) . …
3: 26.17 The Twelvefold Way
4: 27.14 Unrestricted Partitions
27.14.3 1 f ( x ) = n = 0 p ( n ) x n ,
27.14.6 p ( n ) = k = 1 ( - 1 ) k + 1 ( p ( n - ω ( k ) ) + p ( n - ω ( - k ) ) ) = p ( n - 1 ) + p ( n - 2 ) - p ( n - 5 ) - p ( n - 7 ) + ,
27.14.7 n p ( n ) = k = 1 n σ 1 ( k ) p ( n - k ) ,
27.14.8 p ( n ) e K n / ( 4 n 3 ) ,
27.14.15 5 ( f ( x 5 ) ) 5 ( f ( x ) ) 6 = n = 0 p ( 5 n + 4 ) x n
5: DLMF Project News
error generating summary
6: 1.4 Calculus of One Variable
Functions of Bounded Variation
With a < b , the total variation of f ( x ) on a finite or infinite interval ( a , b ) is
1.4.33 𝒱 a , b ( f ) = sup j = 1 n | f ( x j ) - f ( x j - 1 ) | ,
1.4.34 𝒱 a , b ( f ) = a b | f ( x ) | d x ,
For further information on total variation see Olver (1997b, pp. 27–29). …
7: 31.14 General Fuchsian Equation
With a 1 = 0 and a 2 = 1 the total number of free parameters is 3 N - 3 . …
8: 26.12 Plane Partitions
A plane partition is totally symmetric if it is both symmetric and cyclically symmetric. The number of totally symmetric plane partitions in B ( r , r , r ) is … The number of totally symmetric self-complementary plane partitions in B ( 2 r , 2 r , 2 r ) is …
9: 18.39 Physical Applications
For (18.39.2) to have a nontrivial bounded solution in the interval - < x < , the constant E (the total energy of the particle) must satisfy …
10: 25.10 Zeros
Riemann developed a method for counting the total number N ( T ) of zeros of ζ ( s ) in that portion of the critical strip with 0 < t < T . …