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FunctionAdvisor/sum_form - return the sum form of a given mathematical function
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Calling Sequence
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FunctionAdvisor(sum_form, math_function)
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Parameters
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sum_form
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literal name; 'sum_form'
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math_function
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Maple name of mathematical function
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Description
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The FunctionAdvisor(sum_form, math_function) command returns the sum form of the function if it exists.
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Examples
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![[StruveL(a, z) = Sum(-((1/2)*I)*(-1)^((1/2)*a+1/2+2*_k1)*z^(a+1+2*_k1)/(exp(((1/2)*I)*a*Pi)*2^(a+2*_k1)*GAMMA(3/2+a+_k1)*GAMMA(3/2+_k1)), _k1 = 0 .. infinity), And((a+3/2)::(Not(nonnegint)))]](/support/helpjp/helpview.aspx?si=7325/file01738/math58.png)
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![[JacobiTheta1(a, z) = Sum(2*z^((_k1+1/2)^2)*sin(a*(2*_k1+1))*(-1)^_k1, _k1 = 0 .. infinity), And(abs(z) < 1)]](/support/helpjp/helpview.aspx?si=7325/file01738/math65.png)
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![[cos(z) = Sum((-1)^_k1*z^(2*_k1)/factorial(2*_k1), _k1 = 0 .. infinity), `with no restrictions on `(z)]](/support/helpjp/helpview.aspx?si=7325/file01738/math72.png)
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The variables used by the FunctionAdvisor command to create the function calling sequences are local variables. Therefore, the previous example does not depend on z.
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To make the FunctionAdvisor command return results using global variables, pass the function call itself.
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![[Stirling1(n, z) = Sum(Sum((-1)^(2*_k1-_k2)*binomial(n-1+_k1, n-z+_k1)*binomial(2*n-z, n-z-_k1)*binomial(_k1, _k2)*_k2^(n-z+_k1)/factorial(_k1), _k2 = 0 .. _k1), _k1 = 0 .. n-z), And(n::nonnegint, z::nonnegint)]](/support/helpjp/helpview.aspx?si=7325/file01738/math99.png)
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