Rel(G)=F0pm(1−p)0+F1pm-1(1−p)1+F2pm-2(1−p)2+…+Fmp0(1−p)m
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ただし、i>d+1においてFi=0で、また、
F0xd+1+F1xd+…Fd+1x0=
h0(x+1)d+1+h1(x+1)d+…+hd+1(x+1)0.
(証明)
Rel(G)=F0pm(1−p)0+F1pm-1(1−p)1+F2pm-2(1−p)2+…+Fmp0(1−p)m
=
F0pm(1−p)0+F1pm-1(1−p)1+F2pm-2(1−p)2+…+Fd+1pm-(d+1)(1−p)d+1
=
pm-(d+1)(
F0pd+1(1−p)0+F1pd(1−p)1+F2pd-1(1−p)2+…+Fd+1p0(1−p)d+1)
=
pm-(d+1)(1−p)d+1(
F0(p/(1−p))d+1+F1(p/(1−p))d+F2(p/(1−p))d-1+…+Fd+1(p/(1−p))0)
=
pm-(d+1)(1−p)d+1(
h0(p/(1−p)+1)d+1+h1(p/(1−p)+1)d+h2(p/(1−p)+1)d-1+…+hd+1(p/(1−p)+1)0)
=
pm-(d+1)(1−p)d+1(
h0(1/(1−p))d+1+h1(1/(1−p))d+h2(1/(1−p))d-1+…+hd+1(1/(1−p))0)
=
pm-(d+1)(
h0(1−p)0+h1(1−p)1+h2(1−p)2+…+hd+1(1−p)d+1)