Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8037)

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/07.22.03.8037.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 19/4}, -z] == ((-2 Sqrt[z] (582574444502675625 - 421856347062150000 z - 51811802025984000 z^2 - 51259519877529600 z^3 + 20175391427788800 z^4 - 2825272153866240 z^5 + 230770606080000 z^6 - 14075681570816 z^7 + 949187772416 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]]^2 + (1747723333508026875 - 3928766501770110000 z - 108480960491904000 z^2 - 69082402701312000 z^3 + 22404946791628800 z^4 - 2993461835857920 z^5 + 240362811555840 z^6 - 14553496682496 z^7 + 906238099456 z^8 + 68719476736 z^9) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (1747723333508026875 - 200290056952986000 z + 32382376266240000 z^2 + 57790086875136000 z^3 - 20992813999718400 z^4 + 2888929357332480 z^5 - 234533802737664 z^6 + 14286134968320 z^7 - 932007903232 z^8 - 68719476736 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(95864998802227200 Sqrt[2] z^(13/4))

Standard Form

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MathML Form

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<sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]