NUMERICAL CALCULATION OF BESSEL FUNCTIONS

A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The trapezoidal rule, applied to suitable integral representations, may become the method of choice for evaluation of the many special functions of mathematical physics.

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MORE SPECIAL FUNCTIONS TRAPPED

International Journal of Modern Physics C ◽

10.1142/s0129183113500046 ◽

2013 ◽

Vol 24 (02) ◽

pp. 1350004

Author(s):

CHARLES SCHWARTZ

Keyword(s):

Hypergeometric Function ◽

Bessel Functions ◽

Special Functions ◽

Mathematical Physics ◽

Confluent Hypergeometric Function ◽

Trapezoidal Rule ◽

Integral Representations ◽

Gamma Functions ◽

Incomplete Gamma Functions

We extend the technique of using the trapezoidal rule for efficient evaluation of the special functions of mathematical physics given by integral representations. This technique was recently used for Bessel functions, and here we treat incomplete gamma functions and the general confluent hypergeometric function.

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Special functions, infinite divisibility and transcendental equations

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100055912 ◽

1979 ◽

Vol 85 (3) ◽

pp. 453-464 ◽

Cited By ~ 5

Author(s):

Mourad E. H. Ismail ◽

C. Ping May

Keyword(s):

Bessel Functions ◽

Special Functions ◽

Infinite Divisibility ◽

Probability Density Functions ◽

Integral Representations ◽

Density Functions ◽

Modified Bessel Functions ◽

Explicit Formulas ◽

Linear Combinations ◽

Transcendental Equations

AbstractWe establish integral representations for quotients of Tricomi ψ functions and of several quotients of modified Bessel functions and of linear combinations of them. These integral representations are used to prove the complete monotonicity of the functions considered and to prove the infinite divisibility of a three parameter probability distribution. Limiting cases of this distribution are the hitting time distributions considered recently by Kent and Wendel. We also derive explicit formulas for the Kent–Wendel probability density functions.

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Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions

Mathematical Problems in Engineering ◽

10.1155/2020/8614841 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Fuli He ◽

Ahmed Bakhet ◽

Mohamed Akel ◽

Mohamed Abdalla

Keyword(s):

Zeta Function ◽

Infinite Series ◽

Hypergeometric Functions ◽

Recurrence Relations ◽

Special Functions ◽

Mathematical Physics ◽

Integral Representations ◽

Digamma Function ◽

Polygamma Function

In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We present several properties, recurrence relations, infinite series, and integral representations for these functions. Furthermore, we establish identities involving hypergeometric functions in terms of degenerate digamma function.

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