Download CURRENT Medical Diagnosis and Treatment 2012, Fifty-First by Stephen J. McPhee PDF

By Stephen J. McPhee

The no 1 every year up to date textual content in inner medicine!

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Extra info for CURRENT Medical Diagnosis and Treatment 2012, Fifty-First Edition

Example text

Br q (a1 ) · · · q (ap ) q (b1 ) · · · q (br ) . 49) In the same way as the function plays a basic role in complex analysis, the q function is fundamental for q-calculus. The reason is the close connection to the q-factorial. 1 cd Eq (x) Definition 8 ∞ Eq (z) ≡ k=0 Diagram 1 1 k z . {k}q ! 7 The first q-functions 23 Diagram 2 Diagram 3 The speed can be compared to the q-derivative. 2 ⎧ ϕ(x)−ϕ(qx) ⎪ ⎨ (1−q)x , (Dq ϕ)(x) ≡ dϕ dx (x), ⎪ ⎩ dϕ dx (0), if q ∈ C\{1}, x = 0, if q = 1, if x = 0. 52) 0 < |q| < 1, a ∈ R.

One example is the book Die Elemente der Mathematik by Johann Friedrich Lorenz (1737–1807) from 1797, which treated such diverse subjects as refraction, parallax, geography, the atmosphere of the moon. Elementary trigonometric formulas were given, and these trigonometric functions were used to treat the physics involved. This was natural since many earlier mathematicians, like the Bernoullis, were both physicians and physicists. John Bernoulli (1) has in fact even written a memoir about mathematical medicine.

In the 1956 issue there is a report on the hypergeometric functions of three variables by Krishna Ji Srivastava, which refers to Saran. These two mathematicians were probably unaware of the articles by Horn. H. M. Srivastava was born in India, settled in Canada in the early seventies, but travelled frequently to India until 1985. He was a good friend of and therefore also inspired by Gould of the American–Austrian School. Srivastava left India permanently in the 1980s and without its founder the School quickly dwindled.

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