Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equation - 1st Edition - ISBN: 9780080101613, 9781483184999

Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equation

1st Edition

Mathematical Tables Series

Authors: L. N. Nosova S. A. Tumarkin
eBook ISBN: 9781483184999
Imprint: Pergamon
Published Date: 1st January 1965
Page Count: 126
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Description

Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the "Strela" highspeed electronic computer.

This book will be of great value to mathematicians, researchers, and students.

Table of Contents


Foreword

1. Introduction

2. Some Properties of the Tabulated Functions

3. Arrangement and Computation of the Tables, and Methods for their Use

4. Application of the Functions en(t) and ẽn(t) to the Asymptotic Solution of Differential Equations

5. An Example of the Asymptotic Solution of a Differential Equation

6. Use of the Tables in Connection with Toroidal Shells and in Solving Other Problems

References

Table I. The Functions en(t) for t = is and their Derivatives with Respect to s;en(is) = R(en) + iI(en); e'n = den/ds = R(e'n) + iI(e'n); 0 ≦ s ≦ 9; n = 0, 1, 2

Table II. The Functions e0(t), e1(t), e2(t) and their Derivatives for Real t; 0 ≦ t ≦ 10; -1 ≦ t ≦ 0

Table III. The Functions ẽ0(t), ẽ1(t), ẽ2(t) and their Derivatives for Real t; -10 ≦ t ≦ 0; 0 ≦ t ≦ 1

Supplement. Table IV. The Airy Functions h1(t) and h2(t) for t= is and their Derivatives h'1 and h'2 with Respect to s; d2hk/dt2+thk = 0; hk = R(hk) + iI(hk); h'k = dhk/ds = R(h'k) + iI(h'k); 0 ≦ s ≦ 6; k = 1, 2

Volumes in the Mathematical Tables Series

Details

No. of pages:
126
Language:
English
Copyright:
© Pergamon 1965
Published:
Imprint:
Pergamon
eBook ISBN:
9781483184999

About the Author

L. N. Nosova

S. A. Tumarkin