About the Project
NIST

infinite

AdvancedHelp

(0.000 seconds)

1—10 of 108 matching pages

1: 4.11 Sums
For infinite series involving logarithms and/or exponentials, see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §44), and Prudnikov et al. (1986a, Chapter 5).
2: 4.22 Infinite Products and Partial Fractions
§4.22 Infinite Products and Partial Fractions
3: 4.36 Infinite Products and Partial Fractions
§4.36 Infinite Products and Partial Fractions
4: 25.8 Sums
25.8.1 k = 2 ( ζ ( k ) - 1 ) = 1 .
25.8.2 k = 0 Γ ( s + k ) ( k + 1 ) ! ( ζ ( s + k ) - 1 ) = Γ ( s - 1 ) , s 1 , 0 , - 1 , - 2 , .
25.8.5 k = 2 ζ ( k ) z k = - γ z - z ψ ( 1 - z ) , | z | < 1 .
25.8.9 k = 1 ζ ( 2 k ) ( 2 k + 1 ) 2 2 k = 1 2 - 1 2 ln 2 .
25.8.10 k = 1 ζ ( 2 k ) ( 2 k + 1 ) ( 2 k + 2 ) 2 2 k = 1 4 - 7 4 π 2 ζ ( 3 ) .
5: 25.2 Definition and Expansions
25.2.1 ζ ( s ) = n = 1 1 n s .
§25.2(ii) Other Infinite Series
25.2.4 ζ ( s ) = 1 s - 1 + n = 0 ( - 1 ) n n ! γ n ( s - 1 ) n ,
§25.2(iv) Infinite Products
25.2.11 ζ ( s ) = p ( 1 - p - s ) - 1 , s > 1 ,
6: Sidebar 5.SB1: Gamma & Digamma Phase Plots
This pattern is analogous to one that would be seen in fluid flow generated by a semi-infinite line of vortices. …
7: 5.8 Infinite Products
§5.8 Infinite Products
8: 8.15 Sums
For sums of infinite series whose terms include incomplete gamma functions, see Prudnikov et al. (1986b, §5.2).
9: 1.9 Calculus of a Complex Variable
§1.9(v) Infinite Sequences and Series
This sequence converges pointwise to a function f ( z ) if …
§1.9(vii) Inversion of Limits
Dominated Convergence Theorem
10: 24.8 Series Expansions
§24.8(i) Fourier Series
If n = 1 , 2 , and 0 x 1 , then …
§24.8(ii) Other Series
24.8.9 E 2 n = ( - 1 ) n k = 1 k 2 n cosh ( 1 2 π k ) - 4 k = 0 ( - 1 ) k ( 2 k + 1 ) 2 n e 2 π ( 2 k + 1 ) - 1 , n = 1 , 2 , .