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picture1_Academic Pdf 182150 | Special Functions Ppt By D Kamlesh Bisht Converted


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File: Academic Pdf 182150 | Special Functions Ppt By D Kamlesh Bisht Converted
dr kamlesh bisht mathematics mob no 8279829875 special functions unit 12 legendre polynomial and functions dr kamlesh bisht academic consultant department of mathematics uttarakhand open university haldwani dr kamlesh bisht ...

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                                                                  Dr. Kamlesh Bisht
                                                                   (Mathematics)
                                                                 Mob. No.-8279829875
                             SPECIAL FUNCTIONS
                UNIT –12: LEGENDRE POLYNOMIAL AND FUNCTIONS
                               Dr. Kamlesh Bisht
                               Academic Consultant
                            Department of Mathematics
                       Uttarakhand Open University, Haldwani
                                                                                       Dr. Kamlesh Bisht
                                                                                        (Mathematics)
                                                                                     Mob. No.-8279829875
                                 CONTENTS
        1.   LEGENDRE’S EQUATION
        1.1. LEGENDRE’S POLYNOMIAL P (x)
                                           n
        1.2. LEGENDRE’S FUNCTION OF THE SECOND KIND i.e. Q (x)
        1.3 GENERAL SOLUTION OF LEGENDRE’S EQUATION                 n
        2. RODRIGUE’S FORMULA
        3. A GENERATING FUNCTION OF LEGENDRE’S     POLYNOMIAL
        4. ORTHOGONALITY OF LEGENDRE POLYNOMIALS
        5. RECURRENCE FORMULAE
        6. NUMERICAL PROBLEMS
        7. LEGENDRE’S POLYNOMIALS APPLICATIONS
        8. NUMERICAL PROBLEMS
                                                   Dr. Kamlesh Bisht
                                                    (Mathematics)
                                                  Mob. No.-8279829875
                 1. LEGENDRE’S EQUATION
                                                                                                               Dr. Kamlesh Bisht
                                                                                                                (Mathematics)
                                                                                                            Mob. No.-8279829875
  Now, 
                                         m             −−12
                                    y = x  (a +a x +a x +...)                                         ...(2)
                                              0     1          2
                                        
                                                mr−
            =                  y          a x
                                        r
                                       r=0
                                   dy       
                                                            m−−r l
            so that                     =−a(m r)
                                   dx      r
                                           r=0
                                     2
                                   dy                                        mr−−2
             and                         =−a(m r)(m−−r l)x
                                   dx2       r
                                            r=0                                                                           
            Substituting these values in (1), we have 
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...Dr kamlesh bisht mathematics mob no special functions unit legendre polynomial and academic consultant department of uttarakhand open university haldwani contents s equation p x n function the second kind i e q general solution rodrigue formula a generating orthogonality polynomials recurrence formulae numerical problems applications now m y mr r dy l so that dx substituting these values in we have...

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