
Laguerre’s Equation Consider Laguerre’s Equation
Polynomial solutions of Laguerre’s equation are called Laguerre polynomials and are denoted by
to show that
Assume that
Determine the Laguerre polynomials

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Chapter 16 Solutions
EBK MULTIVARIABLE CALCULUS
- Explain the relationship between 12.3.6, (case A of 12.3.6) and 12.3.7arrow_forwardExplain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse 12.4.2 to determine whether the infinite series on the right side of equation 12.6.5, 12.6.6 and 12.6.7 converges for every real number x.arrow_forward
- use Corollary 12.6.2 and 12.6.3 to derive 12.6.4,12.6.5, 12.6.6 and 12.6.7arrow_forwardExplain the focus and reasons for establishment of 12.5.1(lim(n->infinite) and sigma of k=0 to n)arrow_forwardExplain the focus and reasons for establishment of 12.5.3 about alternating series. and explain the reason why (sigma k=1 to infinite)(-1)k+1/k = 1/1 - 1/2 + 1/3 - 1/4 + .... converges.arrow_forward
- Explain the key points and reasons for the establishment of 12.3.2(integral Test)arrow_forwardUse identity (1+x+x2+...+xn)*(1-x)=1-xn+1 to derive the result of 12.2.2. Please notice that identity doesn't work when x=1.arrow_forwardExplain the key points and reasons for the establishment of 11.3.2(integral Test)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
