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Interpolation of functions - Example

Example [1]

The table of values of full elliptic integral

is given; find К (78º 30’).

Values of full elliptic integral K ( α )

α

K ( α )

ΔK

Δ 2 K

Δ 3 K

Δ 4 K

Δ 5 K

Δ 6 K

75º

2.76806

6461

76º

2.83267

528

6989

84

77º

2.90256

612

19

7601

103

13

78º

2.97857

715

32

– 5

8316

135

8

79º

3.06173

850

40

18

9166

175

26

80º

3.15339

1025

66

– 1

10191

241

25

81º

3.25530

1266

91

43

11457

332

68

82º

3.36987

1598

159

13055

491

83º

3.50042

2089

15144

84º

3.65186

S o l u t i o n .   According to data of the table it is accepted х 0 = 78º ; h =1º ; х = 78º 30’, from here q = 0.5. Being limited to differences of the fifth order, from Stirling’s interpolation formula we have:


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