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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: 6. Gamma Function and Related Functions PHILIP J. DAVIS Contents Mathematical Properties. . . . . . . . . . . . . . . . . . . . 6.1. Gamma Function. . . . . . . . . . . . . . . . . . . . 6.2. Beta Function . . . . . . . . . . . . . . . . . . . . . 6.3. Psi (Digamma) Function. . . . . . . . . . . . . . . . . 6.4. Polygamma Functions. . . . . . . . . . . . . . . . . . 6.5. Incomplete Gamma Function. . . . . . . . . . . . . . . 6.6. Incomplete Beta Function. . . . . . . . . . . . . . . . Numerical Methods . . . . . . . . . . . . . . . . . . . . . . 6.7. Use and Extension of the Tables. . . . . . . . . . . . . 6.8. Summation of Rational Series by Means of Polygamma Func- tions. . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . Table 6.1. Gamma, Digamma and Trigamma Functions (1 I s 5 2) . . r(x), In r(x), +(s), +'(s), s=1(.005)2, 10D Table 6.2. Tetragamma and Pentagamma Functions (1 5 2 1 2 ) . . . +"(x), \$J3)(x), 2=1(.01)2, 1OD Table 6.3. Gamma and Digamma Functions for Integer and Half- Integer Values ( I I n l 1 0 1 ) . . . . . . . . . . . . . . . . . . r(n), 11s +(n), 1OD l/r(n), 9s n!/[(27r)*nn+4]e-", 8D r(n++), 8s Inn-+(n), 8D n= 1 (1) 101 Table 6.4. Logarithms of the Gamma Function (1 I n I 1 0 1 ) . . , . . log,, rw, 8s loglo r(n+i), 8s loglo r(n++>, 8s loglo r (n+ 41, 8s In r (n) - (n-+) In n+n, 8D n=1(1)101 Page 255 255 258 258 260 260 263 263 263 264 265 267 27 1 272 2 74 1 National Bureau of Standards. 253 ~~ ~~ ~~~ ~~ 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.