Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8372)

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`=5/2

http://functions.wolfram.com/07.22.03.8372.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 19/4}, z] == ((2 Sqrt[z] (88268855227678125 - 143064326394990000 z + 2112950051372160000 z^2 + 28048124909939097600 z^3 - 20552364181949644800 z^4 + 3235548976172236800 z^5 - 169537332167311360 z^6 + 3438013946265600 z^7 - 27225797689344 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 - (264806565683034375 - 25678212429870000 z + 5399761242395520000 z^2 + 19116252200831385600 z^3 - 18778934441027174400 z^4 + 3135056933604556800 z^5 - 167433504848609280 z^6 + 3421113249955840 z^7 - 27182848016384 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-264806565683034375 + 590598885887010000 z + 4804789049130470400 z^2 + 23917567755755520000 z^3 - 19803858581038694400 z^4 + 3194458780572057600 z^5 - 168688337257758720 z^6 + 3431234340388864 z^7 - 27208617820160 z^8 + 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (39999920398663680000 Sqrt[2] z^(13/4))

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]