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Ⅰ．SHORT HISTORICAL INTRODUCTION;FUNCTIONS OF THE FIRST THREE KINDS OF ORDER ZERO,J0(z),Y0(z),H(1),(2)0(z);APPLICATIONS 1

Ⅱ．FUNCTIONS OF THE FIRST THREE KINDS OF ORDER v,Jv(z),Yv(z),H(1),(2)v(z);CYLINDER FUNCTIONS;ZEROS OF Jv(z);WRONSKIAN RELATION;APPLICATIONS 22

Ⅲ．EXPANSIONS IN BESSEL FUNCTIONS;INTEGRATION;APPLICATIONS 55

Ⅳ．STRUVE FUNCTIONS;INTEGRALS INVOLVING BESSEL,STRUVE,AND CIRCULAR FUNCTIONS;COMPLEX VARIABLE;ASYMPTOTIC EXPANSIONS;APPLICATIONS 74

Ⅴ．LOMMEL INTEGRALS FOR PRODUCTS OF TWO BESSEL FUNCTIONS;APPLICATIONS 102

Ⅵ．THE MODIFIED FUNCTIONS Iv(z) AND Kv(z);APPLICATIONS 113

Ⅶ．BER,BEI,KER,KEI,HER,HEI,YER,YEI,STER,AND STEI FUNCTIONS 137

Ⅷ．APPLICATION OF BER,BEI,KER,AND KEI FUNCTIONS 153

APPENDIX Ⅰ．GAMMA AND HYPERGEOMETRIC FUNCTIONS 177

APPENDIX Ⅱ．CONVERGENCE,DIFFERENTIATION AND INTEGRATION OF INFINITE SERIES TERM BY TERM 182

APPENDIX Ⅲ．SINGULAR POINTS OF BESSEL＇S EQUATION,AND OF ITS SOLUTIONS 185

MISCELLANEOUS PROBLEMS 187

LIST OF 367 FORMULAE 190

TABLES 215

REFERENCES 231

INDEX 237