Table 2: The values of 𝐸 ( 𝑛 , 𝑞 , 𝑥 ) = 𝐵 𝑛 , 𝑞 ( 𝑓 ; 𝑥 ) 𝑓 ( 𝑥 ) at some points 𝑥 [ 0 , 1 ] .

𝑥 𝐸 ( 3 , 2 , 𝑥 ) 𝐸 ( 4 , 2 , 𝑥 ) 𝐸 ( 1 0 , 2 , 𝑥 ) 𝐸 ( 1 5 , 2 , 𝑥 ) 𝐸 ( 2 0 , 2 , 𝑥 ) 𝐸 ( 2 5 , 2 , 𝑥 ) 𝐸 ( 3 0 , 2 , 𝑥 )

( 5 𝑞 + 1 ) / 6 𝑞 2 . 3 8 × 1 0 2 1 . 1 1 × 1 0 2 1 1 . 8 −268. 5 . 5 7 × 1 0 3 1 . 1 5 × 1 0 5 2 . 3 9 × 1 0 6
( 1 1 𝑞 + 7 ) / 1 8 𝑞 7 . 2 3 × 1 0 2 1 . 0 7 × 1 0 3 8 . 1 3 −101. 1 . 1 2 × 1 0 3 1 . 2 1 × 1 0 4 1 . 3 2 × 1 0 5
( 𝑞 + 1 ) / 2 𝑞 9 . 9 7 × 1 0 2 1 . 2 0 × 1 0 2 5 . 2 1 4 7 . 4 −368. 2 . 8 0 × 1 0 3 2 . 1 3 × 1 0 4
( 5 𝑞 + 1 3 ) / 1 8 𝑞 0 . 1 5 1 4 . 6 9 × 1 0 2 1 . 4 6 . 6 4 2 4 . 6 8 5 . 6 −293.
( 𝑞 + 5 ) / 6 𝑞 0 . 1 7 2 6 . 5 4 × 1 0 2 0 . 5 2 8 1 . 8 1 4 . 6 1 0 . 6 2 3 . 7
1 / 𝑞 0 . 1 9 8 . 8 9 × 1 0 2 1 . 3 0 × 1 0 3 4 . 0 7 × 1 0 5 1 . 2 7 × 1 0 6 3 . 9 7 × 1 0 8 1 . 2 4 × 1 0 9
( 𝑞 + 1 ) / 2 𝑞 2 0 . 1 8 0 9 . 9 8 × 1 0 2 0 . 0 5 2 7 . 5 9 × 1 0 2 8 . 1 6 × 1 0 2 8 . 2 9 × 1 0 2 8 . 3 2 × 1 0 2
1 / 𝑞 2 0 . 1 0 3 5 . 5 7 × 1 0 2 9 . 7 5 × 1 0 4 3 . 0 5 × 1 0 5 9 . 5 4 × 1 0 7 2 . 9 8 × 1 0 8 9 . 3 1 × 1 0 1 0
( 𝑞 + 1 ) / 2 𝑞 3 5 . 3 8 × 1 0 2 2 . 3 8 × 1 0 2 7 . 9 2 × 1 0 5 5 . 8 9 × 1 0 7 4 . 3 7 × 1 0 9 3 . 2 4 × 1 0 1 1 2 . 4 0 × 1 0 1 3
1 / 𝑞 3 2 . 2 1 × 1 0 2 7 . 1 5 × 1 0 3 2 . 2 2 × 1 0 6 2 . 1 7 × 1 0 9 2 . 1 2 × 1 0 1 2 2 . 0 7 × 1 0 1 5 2 . 0 2 × 1 0 1 8
( 𝑞 + 1 ) / 2 𝑞 4 1 . 2 0 × 1 0 2 3 . 0 4 × 1 0 3 1 . 7 2 × 1 0 7 4 . 0 1 × 1 0 1 1 9 . 2 9 × 1 0 1 5 2 . 1 5 × 1 0 1 8 4 . 9 9 × 1 0 2 2
1 / 𝑞 4 5 . 0 9 × 1 0 3 9 . 0 5 × 1 0 4 4 . 6 4 × 1 0 9 1 . 4 2 × 1 0 1 3 4 . 3 4 × 1 0 1 8 1 . 3 2 × 1 0 2 2 4 . 0 4 × 1 0 2 7
( 𝑞 + 1 ) / 2 𝑞 5 2 . 8 × 1 0 3 3 . 8 3 × 1 0 4 3 . 5 4 × 1 0 1 0 2 . 5 7 × 1 0 1 5 1 . 8 6 × 1 0 2 0 1 . 3 5 × 1 0 2 5 9 . 7 8 × 1 0 3 1
1 / 𝑞 5 1 . 2 2 × 1 0 3 1 . 1 4 × 1 0 4 9 . 3 5 × 1 0 1 2 8 . 9 6 × 1 0 1 8 8 . 5 5 × 1 0 2 4 8 . 1 5 × 1 0 3 0 7 . 7 7 × 1 0 3 6
( 𝑞 + 1 ) / 2 𝑞 6 6 . 7 7 × 1 0 4 4 . 8 1 × 1 0 5 7 . 0 8 × 1 0 1 3 1 . 6 1 × 1 0 1 9 3 . 6 4 × 1 0 2 6 8 . 2 5 × 1 0 3 3 1 . 8 7 × 1 0 3 9
1 / 𝑞 6 2 . 9 8 × 1 0 4 1 . 4 3 × 1 0 5 1 . 8 6 × 1 0 1 4 5 . 5 6 × 1 0 2 2 1 . 6 6 × 1 0 2 9 4 . 9 4 × 1 0 3 7 1 . 4 7 × 1 0 4 4
1 / 𝑞 1 9 4 . 3 3 × 1 0 1 2 2 . 6 1 × 1 0 1 7 1 . 1 3 × 1 0 4 9 9 . 2 1 × 1 0 7 7 7 . 4 4 × 1 0 1 0 4 6 . 0 1 × 1 0 1 3 1 4 . 8 6 × 1 0 1 5 8
( 𝑞 + 1 ) / 2 𝑞 2 0 2 . 4 4 × 1 0 1 2 1 . 1 0 × 1 0 1 7 8 . 5 2 × 1 0 5 1 1 . 6 4 × 1 0 7 8 3 . 1 5 × 1 0 1 0 6 6 . 0 3 × 1 0 1 3 4 1 . 1 6 × 1 0 1 6 1
1 / 𝑞 2 0 1 . 0 8 × 1 0 1 2 3 . 2 6 × 1 0 1 8 2 . 2 2 × 1 0 5 2 5 . 6 2 × 1 0 8 1 1 . 4 2 × 1 0 1 0 9 3 . 5 8 × 1 0 1 3 8 9 . 0 4 × 1 0 1 6 7
( 𝑞 + 1 ) / 2 𝑞 2 1 6 . 0 9 × 1 0 1 3 1 . 3 7 × 1 0 1 8 1 . 6 6 × 1 0 5 3 1 . 0 0 × 1 0 8 2 6 . 0 × 1 0 1 1 2 3 . 6 0 × 1 0 1 4 1 2 . 1 5 × 1 0 1 7 0
1 / 𝑞 2 1 2 . 7 1 × 1 0 1 3 4 . 0 7 × 1 0 1 9 4 . 3 3 × 1 0 5 5 3 . 4 3 × 1 0 8 5 2 . 7 1 × 1 0 1 1 5 2 . 1 4 × 1 0 1 4 5 1 . 6 8 × 1 0 1 7 5
1 / 𝑞 4 9 3 . 7 6 × 1 0 3 0 2 . 1 1 × 1 0 4 4 5 . 9 8 × 1 0 1 3 1 3 . 4 × 1 0 2 0 3 1 . 9 3 × 1 0 2 7 5 1 . 0 9 × 1 0 3 4 7 6 . 1 7 × 1 0 4 2 0
( 𝑞 + 1 ) / 2 𝑞 5 0 2 . 1 1 × 1 0 3 0 8 . 8 8 × 1 0 4 5 4 . 4 9 × 1 0 1 3 2 6 . 0 6 × 1 0 2 0 5 8 . 1 4 × 1 0 2 7 8 1 . 0 9 × 1 0 3 5 0 1 . 4 7 × 1 0 4 2 3
1 / 𝑞 5 0 9 . 3 9 × 1 0 3 1 2 . 6 3 × 1 0 4 5 1 . 1 7 × 1 0 1 3 3 2 . 0 8 × 1 0 2 0 7 3 . 6 7 × 1 0 2 8 1 6 . 5 0 × 1 0 3 5 5 1 . 1 5 × 1 0 4 2 8