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Embeddable mathematical and statistical algorithms available for C, C#/.NET, Java™, Fortran and Python applications Table of Contents Introduction ix The IMSL Fortran Numerical Libraries .................................................................................... ix Getting Started .......................................................................................................................... ix Finding the Right Routine .......................................................................................................... x Organization of the Documentation ........................................................................................... x Naming Conventions................................................................................................................. xi Using Library Subprograms .................................................................................................... xii Programming Conventions .................................................................................................... xiii Module Usage ........................................................................................................................ xiii Programming Tips................................................................................................................... xiv Optional Subprogram Arguments ........................................................................................... xiv Error Handling ......................................................................................................................... xv Printing Results ........................................................................................................................ xv Chapter 1: Elementary Functions 1 Routines ..................................................................................................................................... 1 Usage Notes ............................................................................................................................... 1 CARG ........................................................................................................................................ 1 CBRT ......................................................................................................................................... 2 EXPRL ....................................................................................................................................... 4 LOG10 ....................................................................................................................................... 6 ALNREL .................................................................................................................................... 7 Chapter 2: Trigonometric and Hyperbolic Functions 11 Routines ................................................................................................................................... 11 Usage Notes ............................................................................................................................. 11 TAN ......................................................................................................................................... 12 COT ......................................................................................................................................... 13 SINDG ..................................................................................................................................... 16 COSDG .................................................................................................................................... 17 ASIN ........................................................................................................................................ 18 ACOS ....................................................................................................................................... 19 ATAN ...................................................................................................................................... 20 ATAN2 .................................................................................................................................... 21 SINH ........................................................................................................................................ 23 COSH ....................................................................................................................................... 24 TANH ...................................................................................................................................... 25 IMSL MATH LIBRARY Special Functions Table of Contents • i ASINH ..................................................................................................................................... 27 ACOSH .................................................................................................................................... 28 ATANH .................................................................................................................................... 30 Chapter 3: Exponential Integrals and Related Functions 33 Routines ................................................................................................................................... 33 Usage Notes ............................................................................................................................. 33 EI .............................................................................................................................................. 34 E1 ............................................................................................................................................. 35 ENE .......................................................................................................................................... 37 ALI ........................................................................................................................................... 38 SI .............................................................................................................................................. 40 CI .............................................................................................................................................. 41 CIN ........................................................................................................................................... 43 SHI ........................................................................................................................................... 44 CHI ........................................................................................................................................... 45 CINH ........................................................................................................................................ 47 Chapter 4: Gamma Function and Related Functions 49 Routines ................................................................................................................................... 49 Usage Notes ............................................................................................................................. 50 FAC .......................................................................................................................................... 50 BINOM .................................................................................................................................... 52 GAMMA .................................................................................................................................. 53 GAMR ...................................................................................................................................... 56 ALNGAM ................................................................................................................................ 58 ALGAMS ................................................................................................................................