Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9652)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9652.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 3/4}, z] == ((-4 z (2515003981875 - 1053906430500 z + 641053828800 z^2 - 12561018624000 z^3 + 25344417369600 z^4 - 6022590382080 z^5 + 360217313280 z^6 - 6639583232 z^7 + 33554432 z^8) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (7545011945625 - 1724574159000 z + 1246272350400 z^2 - 1783801958400 z^3 + 11056674182400 z^4 - 2904108318720 z^5 + 178061967360 z^6 - 3309305856 z^7 + 16777216 z^8) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (-22635035836875 + 862287079500 z - 2529375433200 z^2 + 4570992518400 z^3 - 32108435251200 z^4 + 95871531571200 z^5 - 23740271493120 z^6 + 1434282098688 z^7 - 26524778496 z^8 + 134217728 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (47327952672000 Sqrt[2] z^(15/4))

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]