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मान लीजिए f(z) = exp, z ∈ ℂ\{0} है। तब f का z = 0 पर अवशेष _______ है।

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CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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अवधारणा:

f(z) का z = 0 पर अवशेष, f(z) के मैक्लॉरिन श्रेणी प्रसार में के गुणांक के बराबर होता है।

व्याख्या:

f(z) = exp

=

=

इसलिए उपरोक्त व्यंजक में का गुणांक

=

=

इसलिए विकल्प (3) सही है।

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