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Expansion of the confluent hypergeometric function in series of Bessel functions

Expansion of the confluent hypergeometric function in series of Bessel functions

An expansion of the confluent hypergeometric function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Phi left-parenthesis a comma c comma z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="normal">Φ<!-- Φ --></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> <mml:mo>,</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\Phi (a,c,z)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in series of functions of the same …