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eulermac

Euler-Maclaurin summation

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

eulermac(expr, x)     or eulermac(expr, x = a..b)

eulermac(expr, x, n)   or eulermac(expr, x = a..b, n)

Parameters

expr

-

expression in x

x

-

independent variable

a, b

-

interval over which the approximation to the sum is computed

n

-

(optional) integer (degree of summation)

Description

• 

The forms eulermac(expr, x) and eulermac(expr, x, n) compute asymptotic approximations to sum(expr, x). If F(x) = eulermac(f(x), x), then Fx+1Fx is asymptotically equivalent to f(x). The order of the approximation is specified by n, and defaults to Order - 1.

• 

The forms eulermac(expr, x=a..b) and eulermac(expr, x=a..b, n) compute nth degree Euler-Maclaurin summation formulas for expr (thus n terms of the expansion are given). If n is not specified, it is assumed to be Order - 1.

Examples

eulermac1x,x

lnx12x112x2+1120x41252x6+O1x8

(1)

eulermac1k,k=1..x

∫1x1kⅆk+γ+12x112x2+1120x41252x6+O1x8

(2)

eulermac1x2,x

1x12x216x3+130x5142x7+O1x9

(3)

eulermac1k2,k=1..x,4

∫1x1k2ⅆk+16π21+12x216x3+130x5+O1x7

(4)

See Also

sum

 


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