6f9e5867-f3cd-4a6f-a4d7-174f22df1144 32 4 5 decimal

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Integration parsing procedure

Pertinent remarks: 1.eval(Σ) behaves same as |local definition. 2. In maths, series Σ are " horror stuff". Mathsoft advice N≤70. 3. This particular example supports N≥50 but won't plot the mid range [granularity]. 4. This explains the search for the low limit of integration wrt the max 'N'

2/π SineIntegral Si(x) N x g 2 π / 1 - (n^x 12 n * +^* 12 n * + (12 n * + (! (* / (n 0 N sum eval * :

x f 50 x g :

0 f 0

Check granularity & departure wrt 'N'.

80 x g 20 x g 10 x g 3 1 sys

'n' not defined
granular in '0' x f x 01 int #

X 0 :

15 decimals X f 20 X g - 0

... computable integration. 20 x g x 01 int 0.309642547501851

... computable integration. 10 x g x 01 int 0.309642547501851

... fair computable integration. 5 x g x 01 int 0.309642547501292

The classical numerical limit demo

2112 * π * exp 1 + 4.17160578044567 10305^*

2113 * π * exp 1 + #

2112 * π * exp 1 - 4.17160578044567 10305^*

2113 * π * exp 1 - #

The granularity test function

x f x 2 π * / 2 π * x / tanh * sqrt :

Granulariry test Smath 5346 XP Home, SP3 64 bit extended FPU.

0.0178 f 0.0532

x 0.0178 ≥

0.0275 - f 0.0662

x 0.0275 - ≤

Smath 6179, Win 7 ... NOT granular 1015 -^f 1.26156626101008 108 -^*

Puzzling different evaluation

x 0.1 : (0.1 ≠

n 50 :

x 0.1 :

1 - (n^0.1 (12 n * +^* 12 n * + (12 n * + (! (* / 1.05039730234827 10263 -^*

1 - (n^x (12 n * +^* 12 n * + (12 n * + (! (* / 0

==========================================

n 48 :

1 - (n^0.1 (12 n * +^* 12 n * + (12 n * + (! (* / 1.07173121808179 10251 -^*

1 - (n^x (12 n * +^* 12 n * + (12 n * + (! (* / 1.07173121808178 10251 -^*