Second order ordinary differential equations

Second order ordinary differential equations tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất...

Second-order ordinary differential equations

Special functions, Sturm-Liouville theory and transforms

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R.S Johnson

Second-order ordinary diferential equations

Special functions, Sturm-Liouville theory and transforms

Download free eBooks at bookboon.com

Second-order ordinary diferential equations: Special functions, Sturm-Liouville theory and transforms

ISBN 978-87-7681-972-9

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Second-order ordinary diferential equations

4

Contents

Contents

Preface to these three texts 9

Part I

he series solution of second order, ordinary diferential equations and

1 Power-series solution of ODEs 13

1.1 Series solution: essential ideas 13

1.2 ODEs with regular singular points 16

2 he method of Frobenius 21

2.1 he basic method 21

2.2 he two special cases 24

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Second-order ordinary diferential equations

5

Contents

3 he Bessel equation and Bessel functions 39

3.1 First solution 39

3.2 he second solution 42

3.3 he modiied Bessel equation 46

4 he Legendre polynomials 49

5 he Hermite polynomials 52

6 Generating functions 55

6.1 Legendre polynomials 56

6.2 Hermite polynomials 57

6.3 Bessel functions 59

Part II

An introduction to Sturm-Liouville theory 65

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