Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8457)

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/07.22.03.8457.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 7/4}, -z] == ((4 z (-7161773243625 - 13095813931200 z + 1621498534580925 z^2 + 1816442066181600 z^3 + 387222472615680 z^4 + 25587343441920 z^5 + 625964941312 z^6 + 5802819584 z^7 + 16777216 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - 2 Sqrt[z] (-42970639461750 - 70389999880200 z + 918644241489975 z^2 + 1610972961998400 z^3 + 372216921373440 z^4 + 25205667102720 z^5 + 622366359552 z^6 + 5792333824 z^7 + 16777216 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-64455959192625 - 93307674259800 z - 419066045798400 z^2 + 5125809995806500 z^3 + 6914327442422400 z^4 + 1524239140469760 z^5 + 101732352196608 z^6 + 2498083160064 z^7 + 23194501120 z^8 + 67108864 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (5075922924072000 Sqrt[2] z^(11/4))

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]