Mathmatical Methods in the Physical Sciences
11 Special Functions
1 INTRODUCTION
2 THE FACTORIAL FUNCTION
3 DEFINITION OF THE GAMMA FUNCTION; RECURSION RELATION
Problems
4 THE GAMMA FUNCTION OF NEGATIVE NUMBERS
5 SOME IMPORTANT FORMULAS INVOLVING GAMMA FUNCTIONS
Problems
6 BETA FUNCTIONS
Problems
7 BETA FUNCTIONS IN TERMS OF GAMMA FUNCTIONS
Problems
8 THE SIMPLE PENDULUM
Problems
9 THE ERROR FUNCTION
Problems
10 ASYMPTOTIC SERIES
Problems
11 STIRLING' S FORMULA
Problems
12 ELLIPTIC INTEGRALS AND FUNCTIONS
Problems
13 MISCELLANEOUS PROBLEMS
12 Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions
1 INTRODUCTION
Problems
2 LEGENDRE' S EQUATION
Problems
3 LEIBNIZ' RULE FOR DIFFERENTIATING PRODUCTS
Problems
4 RODRIGUES' FORMULA
Problems
5 GENERATING FUNCTION FOR LEGENDRE POLYNOMIALS
Problems
6 COMPLETE SETS OF ORTHOGONAL FUNCTIONS
Problems
7 ORTHOGONALITY OF THE LEGENDRE POLYNOMIALS
Problems
8 NORMALIZATION OF THE LEGENDRE POLYNOMIALS
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9 LEGENDRE SERIES
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10 THE ASSOCIATED LEGENDRE FUNCTIONS
Problems
11 GENERALIZED POWER SERIES OR THE METHOD OF FROBENIUS
Problem 11.1
12 BESSEL' S EQUATION
Problems
13 THE SECOND SOLUTION OF BESSEL' S EQUATION
Problems
14 GRAPHS AND ZEROS OF BESSEL FUNCTIONS
Problems
15 RECURSION RELATIONS
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Problems
16 DIFFERENTIAL EQUATIONS WITH BESSEL FUNCTION SOLUTIONS
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17 OTHER KINDS OF BESSEL FUNCTIONS
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18 THE LENGTHENING PENDULUM
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19 ORTHOGONALITY OF BESSEL FUNCTIONS
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20 APPROXIMATE FORMULAS FOR BESSEL FUNCTIONS
Problems
21 SERIES SOLUTIONS; FUCHS' S THEOREM
22 HERMITE FUNCTIONS; LAGUERRE FUNCTIONS; LADDER OPERATORS
Problems
