## Computation of special functionsDeals with the automatic computation of special functions which appear in all areas of engineering and the physical sciences. Contains over 100 computer programs written by the authors and describes the algorithms to provide readers with specific information about each individual program. Consisting of three sections, the first one presents an introduction to the special function to be dealt with, its major properties, and several formulas needed for its computation. The second segment features algorithms for computing the special function and the related quantities and lists corresponding Fortran-77 programs. The final part tabulates representative results to offer a quick outlook on the function's behavior and to check the computed results. The accompanying disk contains all the computer programs discussed in the text. |

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### Contents

HYPERGEOMETRIC AND CONFLUENT | 366 |

References and Further Reading | 424 |

References and Further Reading | 474 |

### Common terms and phrases

30 CONTINUE accuracy algorithm arbitrary order associated Legendre functions associated Legendre polynomials asymptotic expansions backward recurrence CaIcuIate the derivative calculate CALL cem(z CHAPTER characteristic values complex arguments confluent hypergeometric function defined denotes differential equation DIMENSION diskette DOUBLE PRECISION A-H,0-Z elliptic integral En(x ENDIF RETURN END error function Evaluate a sequence expansion coefficients exponential integrals forward recurrence Fractional Order Fresnel integrals gamma function given GO TO 15 hypergeometric function F(a implemented IMPLICIT DOUBLE PRECISION Input integer order integra1 Jacobian elliptic functions Kind for Complex linearly independent solutions MATHEMATICAL TABLES Tables Mathieu functions modified Bessel functions MSTA1 MSTA2 Numerical Computation Oblate radial functions obtain OOOOOOOOOOOOOOOD+OO order and complex Output parabolic cylinder functions polynomial approximations prolate radial functions psi function Purpose Qn(x quadrature Re(z real arguments recurrence relations Routines ca11ed second kind sem(z series expansions spheroidal wave functions SUBROUTINE tabulated in Tables Wronskian relation Yv(z