Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.age1)

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.age1.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(23/4)}, -z] == (Sqrt[2] ((94204863435375 + 167475312774000 z + 25184257560000 z^2 - 36533962967040 z^3 + 11836092280320 z^4 - 3460818493440 z^5 - 8335734865920 z^6 + 15187260211200 z^7 - 448454983680 z^8 + 536870912 z^9) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-94204863435375 - 41868828193500 z + 54565891380000 z^2 - 19787194848960 z^3 + 4702805775360 z^4 - 148852408320 z^5 + 7973311610880 z^6 - 1725733797888 z^7 + 12415139840 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-94204863435375 + 83737656387000 z - 33159272454000 z^2 + 8958472871040 z^3 - 2539794216960 z^4 + 2083933716480 z^5 + 2578584698880 z^6 - 102903054336 z^7 + 134217728 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(94204863435375 z^(1/4))

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]