CRC Standard Mathematical Tables and Formulae, 31st Edition by Daniel Zwillinger

By Daniel Zwillinger

A perennial bestseller, the thirtieth variation of CRC regular Mathematical Tables and Formulae was once the 1st "modern" variation of the guide - tailored to be worthy within the period of non-public pcs and strong hand held units. Now this model will fast identify itself because the "user-friendly" version. With a close desk of contents and an in depth index directory over 6,000 entries, the thirty first version of this highly winning guide makes details even more straightforward to locate.

New within the thirty first edition:

Game thought and balloting power
Heuristic seek techniques
Quadratic fields
Reliability
Risk research and determination rules
A desk of options to Pell's equation
A desk of irreducible polynomials in Z2[x]
An interpretation of powers of 10
A number of "proofs with no words"
Representations of teams of small order
Counting principles
Tesselations and tilings
…and a lot more!

An vital, updated source, CRC average Mathematical Tables and Formulae, thirty first version makes it easy to discover the equations, tables, and formulae you wish frequently.

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Extra resources for CRC Standard Mathematical Tables and Formulae, 31st Edition

Example text

Consider ´Üµ Ü Ø . Then 3. For Ë Ò Ò ½ ½ ½ ½ ½ ½ ´Üµ ½ Hence, Ë converges for Ø 4. The sum Ƚ Ò ½ Ü Ë ½ Ü ÜØ ½ Ø ½ diverges for Ø ½ for Ø ½ ½. ½ ¾ Ò´ÐÓ Òµ converges for × × ½ by the integral test. ´ µÒ ´ ·½µ ´ ·Ò ½µ where is not ¼ or a negative integer. Then 5. Let Ò Ò Ò ½ ´ · ½µ Ò · ´ · ½µ Ò¾ ´½ · ½ Òµ. By Gauss’s test, the series Ò·½ Ò ¼. 1 Bessel series ½ 1. Fourier–Bessel series: ½ 2. Neumann series: 3. Kapteyn series: ½ Ò 4. Schlo¨ milch series: ¼ Ò ½ ´ ·Ò ´ · ÒµÞ Ò ´ÒÞ µ  ·Ò ´¾µ ´ ½·½µ Ƚ ½ Þ 2.

1, 2, 6, 22, 101, 573, 3836, 29228, 250749, 2409581, 25598186, 296643390, 3727542188, 50626553988, 738680521142 Kendall–Mann numbers: maximal inversions in permutation of Ò letters, Ò ½ 53. 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000 Factorial numbers: Ò , Ò ¼ 54. 1, 2, 7, 42, 429, 7436, 218348, 10850216, 911835460, 129534272700, 31095744852375, 12611311859677500, 8639383518297652500 É Robbins numbers: Ò ¼½ ´¿ · ½µ ´Ò · µ , Ò ½ 55.

13. 14. ¼ ´ ½µ ¾Ò¡ ½ ¾Ò·½ Ò·½ Ñ¡ Ò¡ Ñ·Ò· ¡ Ñ·Ò¡¾ ¼ Ñ·Ò Ñ ÈÒ ½ ½ ¾ Ü ½ Ò × ¾ ¾ÜÒ × ¾ Ü ¼ × ¾ ÈÒ ÈÒ ½ Ò Ò ¼× Ò ¼ ¼ ´ ½µ Ó× Ò ¾Ò ½ Ƚ ½ ½ ´ · µ´ · µ ÓØ´ µ ÓØ´ µ Ƚ × Ò ´ Ô¾µ·× Ò´ Ô¾µ ½ ½ ¼ · ¾ · ¾ ¿ Ô¾ Ó× ´ Ô¾µ Ó×´ Ô¾µ Ƚ ½ ½ ½ ¾ ½ ¾ Ƚ ½ ¼ ´ ·½µ ½ Ƚ ½ ½ ¼ ´ ·½µ´ ·¾µ Ƚ ½ ½ ¼ ´ ·½µ´ ·¾µ´ ·¿µ ½ Ƚ ½ ½ ¼ ´ ·½µ¡¡¡´ ·Ôµ Ô¡Ô 15. 43. . so slowly that it reµ¾ ¿ quires ½¼¿ ½ ¡½¼ terms to give two-decimal accuracy ÐÓ ½ ½ diverges, but the partial sums exceed 10 only ¿ ÐÓ ´ÐÓ ÐÓ µ after a googolplex of terms have appeared Ô È½ ´ ½µ ¾ ½ 17.

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