Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8468)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8468.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 19/4}, z] == ((2 Sqrt[z] (21555254446598998125 + 69776051753337930000 z + 80892378687043123200 z^2 + 280715319195936768000 z^3 - 112589522381566771200 z^4 + 11038345556687585280 z^5 - 393956736903413760 z^6 + 5788362858299392 z^7 - 34733400522752 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 - (64665763339796994375 + 145436461950149370000 z + 150469614938061619200 z^2 + 225096867347621068800 z^3 - 106290128842525900800 z^4 + 10801451899646115840 z^5 - 390396551941324800 z^6 + 5766769910218752 z^7 - 34690450849792 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (57156736173797885625 + 109466766041135302800 z + 121686123448976486400 z^2 + 256251664500804403200 z^3 - 109973794849682227200 z^4 + 10942054794799349760 z^5 - 392523087423209472 z^6 + 5779706351714304 z^7 - 34716220653568 z^8 + 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (348856448619773952000 Sqrt[2] z^(13/4))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]