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The AGT conjecture identifying conformal blocks with the Nekrasov functionsis investigated for the spherical conformal blocks with more than 4 externallegs. The diagram technique which arises in conformal block calculationinvolves propagators and vertices. We evaluated vertices with two Virasoroalgebra descendants and explicitly checked the AGT relation up to the thirdorder of the expansion for the 5-point and 6-point conformal blocks on sphereconfirming all the predictions of arXiv:0906.3219 relevant in this situation.We propose that U(1)-factor can be extracted from the matrix elements of thefree field Vertex operators. We studied the n-point case, and found out thatour results confirm the AGT conjecture up to the third order expansions.

Check of AGT Relation for Conformal Blocks on Sphere