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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: 15. Hypergeometric Functions FRITZ OBERHETTINGER Con tents Mathematical Properties . . . . . . . . . . . . . . . . . . . . 15.1. Gauss Series, Special Elementary Cases, Special Values of the Argument. . . . . . . . . . . . . . . . . . . . 15.2. Differentiation Formulas and Gauss’ Relations for Contiguous Functions. . . . . . . . . . . . . . . . . . . . . . 15.3. Integral Representations and Transformation Formulas . . . 15.4. Special Cases of F(a, b; c; z ) , Polynomials and Legendre Functions. . . . . . . . . . . . . . . . . . . . . . 15.5. The Hypergeometric Differential Equation . . . . . . . . 15.6. Riemann’s Differential Equation . . . . . . . . . . . . 15.7. Asymptotic Expansions . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . Page 556 556 557 558 56 1 562 564 56 5 565 1 National Bureau of Standards. (Prwntly, Oregon State University, Cornallis, Oregon.) 555 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.