Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind
Yan Hong, Bai‐Ni Guo, Feng Qi
Abstract
In the paper, by virtue of a general formula for any derivative of the ratio of two differentiable functions, with the aid of a recursive property of the Hessenberg determinants, the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind.
Topics & Concepts
Bessel functionMathematicsBessel polynomialsSequence (biology)Power seriesSeries (stratigraphy)Struve functionBessel processRecurrence relationDifferentiable functionPure mathematicsRiemann zeta functionGenerating functionFunction (biology)Digamma functionMathematical analysisPower (physics)Orthogonal polynomialsArithmetic zeta functionPhysicsPrime zeta functionClassical orthogonal polynomialsPaleontologyEvolutionary biologyQuantum mechanicsMacdonald polynomialsDifference polynomialsBiologyGeneticsGegenbauer polynomialsAdvanced Mathematical IdentitiesAdvanced Combinatorial MathematicsMathematical functions and polynomials