By Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark
Sleek advancements in theoretical and utilized technological know-how rely on wisdom of the houses of mathematical services, from user-friendly trigonometric services to the multitude of precise services. those services seem every time normal phenomena are studied, engineering difficulties are formulated, and numerical simulations are played. in addition they crop up in statistics, monetary versions, and fiscal research. utilizing them successfully calls for practitioners to have prepared entry to a competent selection of their houses. This guide effects from a 10-year undertaking performed by means of the nationwide Institute of criteria and know-how with a world workforce of professional authors and validators. revealed in complete colour, it really is destined to switch its predecessor, the vintage yet long-outdated guide of Mathematical services, edited by way of Abramowitz and Stegun. incorporated with each reproduction of the publication is a CD with a searchable PDF of every chapter.
"The NIST guide is a good-looking product, with huge pages and massive variety. The ebook is sort of heavy; for comfort, one will be susceptible to put it on a stand, as with an unabridged dictionary. The publication includes various pictures, just about all in colour. References and pass references to books and articles abound. functions to either the mathematical and actual sciences are indicated. The NIST instruction manual is certainly a enormous success, and the numerous, a lot of persons who participated in its construction and dissemination are to be congratulated and thanked."
Philip J. Davis for SIAM News
An notable workforce of editors, affiliate editors and validators up-to-date and prolonged the vintage NBS guide of Mathematical capabilities, edited through Abramowitz and Stegun. The nationwide Institute of criteria and know-how (NIST) and Cambridge college Press are to be congratulated for publishing a treasury. it's eminently readable with transparent, sharp, high-contrast textual content, mathematical notation and coloured graphs and figures, the whole booklet is contained in a CD-ROM with a searchable PDF. From Leibnitz to Hilbert, from sleek technological know-how and engineering to different disparate fields of analysis, capabilities are ubiquitous , interesting and lovely gadgets of human ingenuity. A prerequisite to their use is to appreciate their houses, and this guide offers an immediate and concise answer. It includes an intensive bibliography, a listing of notations, and an index. the final structure for every crew of capabilities contains notation, houses, functions, computation and references. those that paintings with features will savor this handbook.
Barry Masters for Optics & Photonics News
"... a superb product."
J. H. Davenport, Computing reports
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Additional resources for NIST Handbook of Mathematical Functions
1. f (α) = c1 . 6 is an entire function with zeros at zn . 11(ii) Elementary Properties Suppose D is a domain, and A polynomial of degree n with real or complex coefficients has exactly n real or complex zeros counting multiplicity. Every monic (coefficient of highest power is one) polynomial of odd degree with real coefficients has at least one real zero with sign opposite to that of the constant term. A monic polynomial of even degree with real coefficients has at least two zeros of opposite signs when the constant term is negative.
11 F (k)eikθ . 23 σn (θ) = 1 2π 2π Kn (θ − t)f (t) dt. 25 is the Fourier series of f (θ), then the series ∞ F (n)einθ F (0) + 2 n=1 can be extended to the interior of the unit circle as an analytic function P (x, y) dx → 0, ∞ F (n)z n . 14(i)). 37 f (t)P (x − t, y) dt h(x, y) = 2π −∞ is the Poisson integral of f (t). 15(v). 29 |h(x, y) − f (x)| dx = 0. lim y →0+ −∞ Suppose now f (x) is real-valued and integrable on (−∞, ∞). Let 1 i ∞ f (t) dt, π −∞ (x − t) + iy where y > 0 and −∞ < x < ∞. 34). 39 − as y → 0.
50 S(f ) = L (L (f )). 1: Fourier transforms. 3: Fourier sine transforms. 2: Fourier cosine transforms. 5: Mellin transforms. 4: Laplace transforms. ∞ ∞ e f (t) −st xs−1 f (x) dx f (x) f (t) dt 0 0 1 , s 1 n s>0 t n! sn+1 1 1 √ πt 1 √ , s e−at 1 , s+a (s + a) > 0 tn e−at n! 1 , (s + a)n+1 (s + a) > 0 e−at − e−bt b−a 1 , (s + a)(s + b) , s>0 1, 0, ln(a/x), x < a, 0, x≥a s>0 a , + a2 s > | a| s2 s , + a2 s > | a| s2 a , − a2 s > | a| cosh(at) s , s2 − a2 s > | a| t sin(at) 2as , (s2 + a2 )2 s > | a| t cos(at) s2 − a2 , (s2 + a2 )2 s > | a| cos(at) sinh(at) e−bt − e−at t ln s+a , s+b 2(1 − cosh(at)) t ln 1 − a2 , s2 (s + a) > 0 2(1 − cos(at)) t ln 1 + a2 , s2 s>0 sin(at) t arctan a , s s>0 s>0 as , s2 a ≥ 0, s>1 0 < s < 1, (Cauchy p.
NIST Handbook of Mathematical Functions by Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark