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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), 23/4}, z] == (19 (2 Sqrt[z] (8754746870244375 + 10119307880682000 z + 2316511413216000 z^2 + 248033099059200 z^3 + 16128258539520 z^4 + 781886423040 z^5 + 28370272256 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 3 (8754746870244375 + 23459874540102000 z + 8311385418336000 z^2 + 1191294829670400 z^3 + 95037736550400 z^4 + 5148272230400 z^5 + 222650433536 z^6 + 5100273664 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (26264240610733125 + 14349243650742000 z + 2860399128787200 z^2 + 289436087808000 z^3 + 18321304780800 z^4 + 873773137920 z^5 + 30349983744 z^6 + 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(500548239360 Sqrt[2] z^(17/4))

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]