Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afi4)

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`=-9/2

http://functions.wolfram.com/07.22.03.afi4.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), -(19/4)}, z] == (1/(215571769875 z^(1/4))) (Sqrt[2] ((215571769875 - 383238702000 z + 58398278400 z^2 + 82819376640 z^3 + 27201968640 z^4 + 15100968960 z^5 + 133524357120 z^6 + 12985565184 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (71857256625 - 31936558500 z - 41365447200 z^2 - 15012486720 z^3 - 3505582080 z^4 + 2384363520 z^5 + 9405726720 z^6 + 180355072 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (215571769875 + 191619351000 z + 76647740400 z^2 + 21766631040 z^3 + 7550484480 z^4 + 14306181120 z^5 + 2846883840 z^6 + 8388608 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]