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Any soluhon äf thuis equation is called Legendre's clifterential equation Considir the (1-x²) Y" - 2xy n-constant Any saluhion tuis equation is° called k = ncnt2). Ligendre's function. Let %3D 8.1. Subetitute Eamx in Legendre's equation & aive at S-2 S-0 Q.2 Find a generul formula lby equating x, 'x' & x"!, n>2 celticients aqhal to zero. Show that fom yex)=DQ0Y,(x) + a, y,(x) y,cx) contains only even powers ofx ,cx) Contains onlyodd powers x series solutron is the cohene while

Any soluhon äf thuis equation is called Legendre's clifterential equation Considir the (1-x²) Y" - 2xy n-constant Any saluhion tuis equation is° called k = ncnt2). Ligendre's function. Let %3D 8.1. Subetitute Eamx in Legendre's equation & aive at S-2 S-0 Q.2 Find a generul formula lby equating x, 'x' & x"!, n>2 celticients aqhal to zero. Show that fom yex)=DQ0Y,(x) + a, y,(x) y,cx) contains only even powers ofx ,cx) Contains onlyodd powers x series solutron is the cohene while

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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Any saluhion d this' equation is" called Considir the Legendre's clifterential equation (1-x²) Y" - 2xy Any saluhion tis equation is" called gendre's function. 8.1. n-constant Let Eamx in equation & arive at k = ncnt2). Legendr's %3D Substitute | S-2 S-0 Q.2 Find a generel formula for as y equating x ceticients qual to x 'x' & x", na2 zero. Show that fom yex)=DQ0Y,(x) + a, y,(x) y,cx) contains only even powers ofx ,cx) Contains only-odd powers x series sl utron is the cohene while
Transcribed Image Text:Any saluhion d this' equation is" called Considir the Legendre's clifterential equation (1-x²) Y" - 2xy Any saluhion tis equation is" called gendre's function. 8.1. n-constant Let Eamx in equation & arive at k = ncnt2). Legendr's %3D Substitute | S-2 S-0 Q.2 Find a generel formula for as y equating x ceticients qual to x 'x' & x", na2 zero. Show that fom yex)=DQ0Y,(x) + a, y,(x) y,cx) contains only even powers ofx ,cx) Contains only-odd powers x series sl utron is the cohene while
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