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 New Online Book! Handbook of Mathematical Functions (AMS55) Conversion & Calculation Home >> Reference Information Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55) Purchase the electronic edition of this book in Adobe PDF format! FIRST | PREVIOUS | NEXT | LAST | CONTENTS | PAGE | ABOUT | SMALL | MEDIUM | LARGE Below is the OCR-scanned text from this page: 18 . Weierstrass Ellip tic and Functions THOMAS H . SOUTHARD Contents Related Mathematical Properties . . . . . . . . . . . . . . . . . . . . Special Values and Relations . . . . . . . . . . . . . 18.4. Addition and Multiplication Forrhulas . . . . . . . . . 18.5. Series Expansions . . . . . . . . . . . . . . . . . . . Derivatives and Differential Equations . . . . . . . . . 18.7. Integrals . . . . . . . . . . . . . . . . . . . . . . 18.8. Conformal Mapping . . . . . . . . . . . . . . . . . 18.9. Relations with Complete Elliptic Integrals K and K’ and Their Parameter m and with Jacobi’s Elliptic Functions . 18.10. Relations with Theta Functions . . . . . . . . . . . . 18.11. Expressing any Elliptic Function in Terms of @ and @’ . . 18.12. CaseA=O . . . . . . . . . . . . . . . . . . . . . . 18.13. Equianharmonic Case (g2 = 0. g3 = 1) . . . . . . . . . . . 18.14. Lemniscatic Case (g2=1. g3=0) . . . . . . . . . . . . . 18.15. Pseudo-Lemniscatic Case (g2= - 1. g3=O) . . . . . . . Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 18.16. Use and Extension of the Tables . . . . . . . . . . . . 18.1. Definitions. Symbolism. Restrictions and Conventions . . 18.2. Homogeneity Relations. Reduction Formulas and Processes . 18.3. 18.6. References . . . . . . . . . . . . . . . . . . . . . . . . . . Pase 629 629 63 1 633 635 635 640 641 642 649 650 651 651 652 658 662 663 663 670 1 University of California. National Bureau of Standards. and California State College at Hayward . 627 .. The page scan image above, and the text in the text box above, are contributions of the National Institute of Standards and Technology that are not subject to copyright in the United States.