The name is absent

Substituting for Xg in the Euler-Lagrange equation for the second segment leads to
an expression for p₂(r)X⅜(r), from which an expression for similar to eqn. 7.14
can be obtained. Repeating this procedure through the ∖^th backbone segment in the
chain gives

3 — ɪ                                         3 — ɪ           3 — ɪ

/   = cxp(,6^f / - [ ⅛ι⅛₂..⅛_j-ιexp[J2A(r_i)]∩Δ^⁺¹∖r_i,r_i+ι)

⅞(^rJ         i=ι   ^j J                 i=ι       i=ι

J-I

= exp(∕352∕√)∕_u(r_j∙),                        (7.15)

i=l

where I₁j is a recursive function, ʃi,ɪ(r) = 1 and ʃij(r) = ʃ dr'ʃij-ɪ(r') exp[∙Dj-ι(r')]Δ^~^lj)(r, r').

For brevity, this procedure is labeled as proc. A, since it is used numerous times in
the derivation.

Similarly, applying proc. A for the linear branch ^ζb_j∙^, from the branch segment ¹b_j

Γ till the backbone segment ‘j’ gives

bj m_j                                              bj m,j           bj τ∏j 1

-■ =exp(β ∑ μ_i) .. / dr_b.ι⅛_b.₂..dr_6j._mj exp[J2 A(r*)] ɪɪ ∆<^v+υ(r_i, r_i+ι)
ʌθlɪ`j`            i=b_jl ''    ∙'                            i=b_jl          i=b_jl

X^1,bjmj (r_j,r_bjτnj) = exp (/3 J2 Mi)^5rj(^rj),                (⁷∙¹⁶)

j=6₃l

where Br_j denotes the branch factor for the branch ⁱb_j∙^, at (backbone) segment ‘j’.
Clearly, Br_j∙(r) = ʃ⅛7₁*J_m3(r')exp[D_bjmj(r')]Δ^^m>(r,r'), where I^._a is the I₁
function for the segment ¹b_j- a' in the branch ^ςb_j∙^,. The branch factors for all the

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