Find Solution using Bessel's formula

x	f(x)
10	20.9848
11	22.9816
12	24.9781
13	26.9743
14	28.9702

x = 12.3
Finding f(2)

Solution:
The value of table for `x` and `y`

x	10	11	12	13	14
y	20.9848	22.9816	24.9781	26.9743	28.9702

Bessel's method to find solution

`h=11-10=1`

Taking `x_0=12` then `p=(x-x_0)/h=(x-12)/1`

The difference table is

`x`	`p=(x-12)/1`	`y`	`Deltay`	`Delta^2y`	`Delta^3y`
10	-2	20.9848
			1.9968
11	-1	22.9816		-0.0003
			1.9965		0
12	0	24.9781		-0.0003
			1.9962		0
13	1	26.9743		-0.0003
			1.9959
14	2	28.9702

`x = 12.3`

`p = (x - x_0)/h = (12.3 - 12)/1 = 0.3`

`y_0=24.9781, Delta y_0=1.9962,Delta^2y_(-1)=-0.0003,Delta^3y_(-1)=0`

Bessel's formula is
`y_p=(y_0+y_1)/2+(p-1/2)*Delta y_0 + (p(p-1))/(2!) * (Delta^2y_(-1)+Delta^2y_(0))/2 + ((p-1/2)p(p-1))/(3!) * Delta^3y_(-1)`

`y_(0.3) = (24.9781+26.9743)/2 + (0.3-1/2)*(1.9962) + (0.3(0.3-1))/(2)*((-0.0003))/2 + ((0.3-1/2)0.3(0.3-1))/(6)*(0)`

`y_(0.3)=25.9762-0.39924 +0.0000315 +0`

`y_(0.3)=25.577`


Solution of Bessel's interpolation is `y(12.3) = 25.577`

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