By Daniel Zwillinger
With over 6,000 entries, CRC typical Mathematical Tables and Formulae, thirty second Edition maintains to supply crucial formulation, tables, figures, and outlines, together with many diagrams, crew tables, and integrals now not on hand on-line. This re-creation comprises very important subject matters which are unusual to a couple readers, equivalent to visible proofs and sequences, and illustrates how mathematical details is interpreted. fabric is gifted in a multisectional layout, with every one part containing a important selection of primary tabular and expository reference material.
New to the thirty second Edition
- A new bankruptcy on Mathematical Formulae from the Sciences that includes crucial formulae from numerous fields, together with acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics
- New fabric on contingency tables, estimators, method strength, runs attempt, and pattern sizes
- New fabric on mobile automata, knot conception, tune, quaternions, and rational trigonometry
- Updated and extra streamlined tables
Retaining the profitable structure of past variants, this accomplished instruction manual is still a useful reference for execs and scholars in mathematical and medical fields.
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Extra info for CRC Standard Mathematical Tables and Formulae
6 FACTORIALS For non-negative integers Ò, the factorial of Ò, denoted Ò , is the product of all posÒ ¡ ´Ò ½µ ¡ ´Ò ¾µ ¡ ¡ ¡ ¾ ¡ ½. If Ò is itive integers less than or equal to Ò; Ò a negative integer (Ò ½ ¾ ) then Ò ¦½. Note that, since the empty product is 1, it follows that ¼ ½. The generalization of the factorial function to non-integer arguments is the gamma function (see page 540). When Ò is an integer, ´Òµ ´Ò ½µ . The double factorial of Ò, denoted Ò , is the product of every other integer: Ò Ò ¡ ´Ò ¾µ ¡ ´Ò µ ¡ ¡ ¡ , where the last element in the product is either 2 or 1, depending on whether Ò is even or odd.
2. The harmonic numbers are ÀÒ . ½ . The rst few values are ½ ¾ ½¾ Asymptotically, ÀÒ ÐÒ Ò · · ¾½Ò . Æ ½ ÜÆ ·½ ÜÒ if Ü ½. 3. 2 GENERAL PROPERTIES 1. Adding or removing a nite number of terms does not affect the convergence or divergence of an in nite series. 2. The terms of an absolutely convergent series may be rearranged in any manner without affecting its value. 3. A conditionally convergent series can be made to converge to any value by suitably rearranging its terms. 4. If the component series are convergent, then ´« Ò · ¬ Ò µ 5.
Adding or removing a nite number of terms does not affect the convergence or divergence of an in nite series. 2. The terms of an absolutely convergent series may be rearranged in any manner without affecting its value. 3. A conditionally convergent series can be made to converge to any value by suitably rearranging its terms. 4. If the component series are convergent, then ´« Ò · ¬ Ò µ 5. Ò ¼ ½ ½ ½ Ò Ò ¼ Ò Ò 6. Summation by parts: let È Ò ¼ Ò « where Ò and È Ò Ò where ËÒ is the Òth partial sum of Ò ·¬ ¼ Ò · Ò ½ Ò ½ · ¡ ¡ ¡ · Ò ¼.
CRC Standard Mathematical Tables and Formulae by Daniel Zwillinger