Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8323)

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`=3/2

http://functions.wolfram.com/07.22.03.8323.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 17/4}, -z] == (Sqrt[Pi] (-7471031633690625 - 17076643734150000 z - 72860346599040000 z^2 + 2720119606364160000 z^3 + 4352191370182656000 z^4 + 1105318443220992000 z^5 + 82447995764736000 z^6 + 2217088961740800 z^7 + 22226455756800 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(7471031633690625 + 9107543324880000 z + 56669158465920000 z^2 + 222371506306252800 z^3 + 64719403912396800 z^4 + 5028078409482240 z^5 + 137281583185920 z^6 + 1385126952960 z^7 + 4294967296 z^8)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-2490343877896875 - 4553771662440000 z + 137761787507097600 z^2 + 260861166036172800 z^3 + 68169657198182400 z^4 + 5127577094062080 z^5 + 138309355438080 z^6 + 1388348178432 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/ (3477531940356096000 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]