Find Solution using Gauss Forward formula

x	f(x)
21	18.4708
25	17.8144
29	17.1070
33	16.3432
37	15.5154

x = 30
Finding f(2)

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

x	21	25	29	33	37
y	18.4708	17.8144	17.107	16.3432	15.5154

Gauss's forward method to find solution

`h=25-21=4`

Taking `x_0=29` then `p=(x-x_0)/h=(x-29)/4`

Now the central difference table is

`x`	`p=(x-29)/4`	`y`	`Deltay`	`Delta^2y`	`Delta^3y`	`Delta^4y`
21	-2	18.4708
			-0.6564
25	-1	17.8144		-0.051
			-0.7074		-0.0054
29	0	17.107		-0.0564		-0.0022
			-0.7638		-0.0076
33	1	16.3432		-0.064
			-0.8278
37	2	15.5154

`x = 30`

`p = (x - x_0)/h = (30 - 29)/4 = 0.25`

`y_0=17.107, Delta y_0=-0.7638,Delta^2y_(-1)=-0.0564,Delta^3y_(-1)=-0.0076,Delta^4y_(-2)=-0.0022`

Gauss's forward interpolation formula is
`y_p=y_0+p Delta y_0 + (p(p - 1))/(2!) * Delta^2y_(-1) + ((p + 1)p(p - 1))/(3!) * Delta^3y_(-1) + ((p + 1)p(p - 1)(p - 2))/(4!) * Delta^4y_(-2)`

`y_(0.25) = 17.107 + (0.25)(-0.7638) + ((0.25)(0.25 - 1))/(2) * (-0.0564) + ((0.25 + 1)(0.25)(0.25 - 1))/(6) * (-0.0076) + ((0.25 + 1)(0.25)(0.25 - 1)(0.25 - 2))/(24) * (-0.0022)`

`y_(0.25)=17.107 -0.1909 +0.0052875 +0.000296875 -0.0000375977`

`y_(0.25)=16.9216`


Solution of Gauss's forward interpolation is `y(30) = 16.9216`

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