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Hi, I am trying to define the function H01 using two recursively defined functions H11 and H12:

memoH11 = {1:0, 2:1/2}
def H11(r1):  
    if memoH11.has_key(r1):
        return memoH11[r1]
    else:
        a = 0
        for j1 in range(1,r1):
            a += j1*(r1 - j1)/r1 * (H11(j1) + H12(j1)) * H11(r1-j1)
        memoH11[r1] = a
        return a 


memoH12 = {1:0, 2:0}
def H12(r2):  
    if memoH12.has_key(r2):
        return memoH12[r2]
    else:
        b = 0
        for j2 in range(1,r2):
            b += j2*(r2 - j2)/r2 * ( H11(j2) + H12(j2) ) * ( H11(r2 - j2) + H12(r2-j2) )
        memoH12[r2] = b
        return b 

def H01(r):    
    return H11(r) + H12(r)

My problem is the following. If I just type

H01(8)

it produces the incorrect value 27/8. But if I type

(H01(6), H01(8))

it result the correct tuple (7/6, 15/4).

So what is the problem in the definition ? Thanks in advance for any help.

Hi, I am trying to define the function H01 using two recursively defined functions H11 and H12:

memoH11 = {1:0, 2:1/2}
def H11(r1):  
    if memoH11.has_key(r1):
        return memoH11[r1]
    else:
        a = 0
        for j1 in range(1,r1):
            a += j1*(r1 - j1)/r1 * (H11(j1) + H12(j1)) * H11(r1-j1)
        memoH11[r1] = a
        return a 


memoH12 = {1:0, 2:0}
def H12(r2):  
    if memoH12.has_key(r2):
        return memoH12[r2]
    else:
        b = 0
        for j2 in range(1,r2):
            b += j2*(r2 - j2)/r2 * ( H11(j2) + H12(j2) ) * ( H11(r2 - j2) + H12(r2-j2) )
        memoH12[r2] = b
        return b 

def H01(r):    
    return H11(r) + H12(r)

My problem is the following. If I just type

H01(8)

it produces the incorrect value 27/8. But if I type

(H01(6), H01(8))

it result results the correct tuple (7/6, 15/4).

So what is the problem in the definition ? Thanks in advance for any help.

Hi, I am trying to define the function compose a code for calculating the numbers H01 using two defined as a sum of the following recursively defined functions H11 and H12:numbers:

H11(r) = \sum_{a + b = r}  a*b/r  (H11(a) + H12(a)) * H11(b)
H12(r) = \sum_{a + b = r}  a*b/r  (H11(a) + H12(a)) * (H11(b) + H12(b))

H01(r) = H11(r) + H12(r)

I ended up with the following code:

memoH11 = {1:0, 2:1/2}
def H11(r1):  
    if memoH11.has_key(r1):
        return memoH11[r1]
    else:
        a = 0
        for j1 in range(1,r1):
            a += j1*(r1 - j1)/r1 * (H11(j1) + H12(j1)) * H11(r1-j1)
        memoH11[r1] = a
        return a 


memoH12 = {1:0, 2:0}
def H12(r2):  
    if memoH12.has_key(r2):
        return memoH12[r2]
    else:
        b = 0
        for j2 in range(1,r2):
            b += j2*(r2 - j2)/r2 * ( H11(j2) + H12(j2) ) * ( H11(r2 - j2) + H12(r2-j2) )
        memoH12[r2] = b
        return b 

def H01(r):    
    return H11(r) + H12(r)

My problem is the following. And here problems start. If I just type

H01(8)

it produces the incorrect value 27/8. But if I type

(H01(6), H01(8))
H01(6), H01(8)

it results the correct tuple (7/6, 15/4).

So what is the problem in the definition how to fix the code ? Thanks in advance for any help.