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...Chapter legendre s polynomials introduction the following second order linear differential equation with variable coefficients is known as named after adrien marie a french mathematician who best for his work in field of elliptic integrals and theory numbers where n non negative integer occurs many physical engineering problems involving spherical geometry gravitation we know that form called or simply this can also be put clearly only singular points are x which regular therefore fuchsian other than e g etc behave like ordinary let series solution putting above values y have an identity various powers it should zero thus equating to coefficient smallest power namely get indicial gives two roots k note unequal differ by now recurrence relation equate next obtain from c indeterminate express terms...