nag_bessel_j_alpha (s18ekc) returns a sequence of values for the Bessel functions  or  for real , non-negative  and .

nag_bessel_j_alpha (s18ekc) evaluates a sequence of values for the Bessel function of the first kind , where  is real and non-zero and  is the order with . The -member sequence is generated for orders when . Note that  is replaced by  when . For positive orders the function may also be called with , since  when . For negative orders the formula

is used to generate the required sequence.

"NE_INT"

On entry, . Constraint: .

"NE_INTERNAL_ERROR"

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.

"NE_OVERFLOW_LIKELY"

The evaluation has been abandoned due to the likelihood of overflow.

"NE_REAL"

On entry, . Constraint: .

"NE_REAL_INT"

On entry, , . Constraint:  when .

"NE_TERMINATION_FAILURE"

The evaluation has been abandoned due to failure to satisfy the termination condition.

"NE_TOTAL_PRECISION_LOSS"

The evaluation has been abandoned due to total loss of precision.

"NW_SOME_PRECISION_LOSS"

The evaluation has been completed but some precision has been lost.

All constants in the underlying functions are are specified to approximately 18 digits of precision. If  denotes the number of digits of precision in the floating-point arithmetic being used, then clearly the maximum number of correct digits in the results obtained is limited by . Because of errors in argument reduction when computing elementary functions inside the underlying functions are, the actual number of correct digits is limited, in general, by , where  represents the number of digits lost due to the argument reduction. Thus the larger the values of  and , the less the precision in the result.

None.