Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7sm)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.a7sm.01

Input Form

HypergeometricPFQ[{-(17/4)}, {5/2, 21/4}, z] == ((-2 Sqrt[z] (-36999394757325 + 88184149653600 z - 161911881331200 z^2 - 4424451771801600 z^3 + 5065934056980480 z^4 - 977765929058304 z^5 + 52230862405632 z^6 - 894963810304 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 3 (-61665657928875 + 190824717283200 z - 308403583488000 z^2 - 1151373378355200 z^3 + 4281955703193600 z^4 - 933357252771840 z^5 + 51454110859264 z^6 - 891205713920 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (-184996973786625 + 177813941104800 z - 485735643993600 z^2 - 1449948692275200 z^3 + 4381429963161600 z^4 - 939460814438400 z^5 + 51563867406336 z^6 - 891742584832 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(3667723341004800 Sqrt[2] z^(15/4))

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]