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The Gamma function I'(r) is a generalization of the factorial function to all real numbers. r(r) = (x – 1)! Vr e N It is defined as: I(x) = t-le-'dt Given the following table I(x) = (x – 1)! 1 1 1 2 4 6 24 (a) Find the coefficients of the Newton Divided Differences Polynomial: PA(x) = a,+a1(x-xo)+a2(r-xo)(x-a1)+a3(x-ro)(x-a1)(r-a2)+a4(x-ro)(x-x1)(x-x2)(x-r3) (b) What is the value of P4(3.5)?

The Gamma function I'(r) is a generalization of the factorial function to all real numbers. r(r) = (x – 1)! Vr e N It is defined as: I(x) = t-le-'dt Given the following table I(x) = (x – 1)! 1 1 1 2 4 6 24 (a) Find the coefficients of the Newton Divided Differences Polynomial: PA(x) = a,+a1(x-xo)+a2(r-xo)(x-a1)+a3(x-ro)(x-a1)(r-a2)+a4(x-ro)(x-x1)(x-x2)(x-r3) (b) What is the value of P4(3.5)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Gamma function I(x) is a generalization of the factorial function to all real numbers. Г() — (х — 1)! VrEN It is defined as: I(x) = fa-le-'dt Given the following table Г() — (х — 1)! 1 1 2 1 3 4 24 (a) Find the coefficients of the Newton Divided Differences Polynomial: P4(x) = ao+a1(x-xo)+a2(x-xo)(x-a1)+a3(x-xo)(x-x1)(x-x2)+a4(x-xo)(x-x1)(x-2)(x-x3) (b) What is the value of P4(3.5)?
Transcribed Image Text:The Gamma function I(x) is a generalization of the factorial function to all real numbers. Г() — (х — 1)! VrEN It is defined as: I(x) = fa-le-'dt Given the following table Г() — (х — 1)! 1 1 2 1 3 4 24 (a) Find the coefficients of the Newton Divided Differences Polynomial: P4(x) = ao+a1(x-xo)+a2(x-xo)(x-a1)+a3(x-xo)(x-x1)(x-x2)+a4(x-xo)(x-x1)(x-2)(x-x3) (b) What is the value of P4(3.5)?
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